#math 2

408 messages · Page 1 of 1 (latest)

unborn forge
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25c^2 + 25c + 4

frail deltaBOT
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unborn forge
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@river plank

river plank
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Hello

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So our question was

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$25c^2 + 25c + 4$

solar pilotBOT
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TheVinkler

river plank
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First I want to explain something ok?

unborn forge
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Yep

river plank
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Just so you understand why we factor things

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sometimes you have equation in the real world that can look something like this:

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$150x^2+789x+9=123$

solar pilotBOT
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TheVinkler

river plank
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just some random numbers ok

unborn forge
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Yeah

river plank
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@stray river I got this, we just moved to the server to have latex

unborn forge
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Yee

stray river
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Yeah I realised, just working out the factorization without intending to send

river plank
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So the idea is to solve these kind of things

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the idea is to able to solve $150x^2+789x-114=0$

solar pilotBOT
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TheVinkler

river plank
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Now a very "easy" way to solve this is make it something like this:

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$(x-a)(x-b)=0$

solar pilotBOT
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TheVinkler

river plank
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The idea is that now we can solve the eqution really easly, one of these sides must be 0 and that is how we solve it ok?

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So this is just the idea of factoring

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Now let's get on how to do it

river plank
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OK

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$25c^2 + 25c + 4$

solar pilotBOT
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TheVinkler

river plank
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What I want you to do is to look at what multiplies c^2 and the constant

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${\color{red}25}c^2 + 25c + {\color{blue}4}$

unborn forge
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Youre like really good at formatting these

solar pilotBOT
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TheVinkler

river plank
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Thank you

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It's not that bad

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I worked with latex for over 100 hours writing things so you get pretty good pretty fast

unborn forge
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Ah

river plank
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So I want you to multply them togather and you get a number ok

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in this case 100

unborn forge
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100?

river plank
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${\color{red}25}\cdot {\color{blue}4}=100$

solar pilotBOT
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TheVinkler

unborn forge
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Oh yeah

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Okay

river plank
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Now is the diffucult part

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${\color{red}25}c^2 + {\color{yellow}25}c + {\color{blue}4}$

solar pilotBOT
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TheVinkler

river plank
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Okay so you want to find now 2 numbers

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A and B, such that $A+B={\color{yellow}25}$ and $A\cdot B=100={\color{red}25}\cdot{\color{blue}4}$

unborn forge
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Yeah yeah i was taught this and to make a T chart

solar pilotBOT
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TheVinkler

unborn forge
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Is it okay if i add something

river plank
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Sure

unborn forge
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Okay so in order to get full marks when there is a question where a and c are perfect square numbers we are supposed to square root them

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Hold on

river plank
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Yes but that is just in case they are like that

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Just if they are the same

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${\color{green} (a+b)}{\color{green}(a+b)}={\color{green}(a+b)}^2$

solar pilotBOT
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TheVinkler

river plank
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And same goes

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${\color{red} (a-b)}{\color{red}(a-b)}={\color{red}(a-b)}^2$

solar pilotBOT
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TheVinkler

river plank
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but

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${\color{green} (a+b)}{\color{red}(a-b)}={\color{yellow}(a^2-b^2)}$

solar pilotBOT
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TheVinkler

river plank
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Ok?

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so it doesn't work every time

river plank
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So back to our orignal question

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${\color{red}25}c^2 + {\color{yellow}25}c + {\color{blue}4}$

solar pilotBOT
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TheVinkler

river plank
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A and B, such that $A+B={\color{yellow}25}$ and $A\cdot B=100={\color{red}25}\cdot{\color{blue}4}$

solar pilotBOT
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TheVinkler

unborn forge
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Mmm

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Okay so basically

unborn forge
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?

river plank
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You can see that we don't have it here right?

unborn forge
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Im sorry wdym have it ? Like no match?

river plank
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Yes

unborn forge
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Im really slow my bad

river plank
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Np

unborn forge
river plank
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Would u like to actaully prove it's not a match?

unborn forge
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Its okay i know it doesnt match

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Its like 20

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And not 25

river plank
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Ye right

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correct

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so

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Can you give me 2 numbers that sum up to 25 and multply to 100?

river plank
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Are you trying to work it out on the calculator?

unborn forge
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Yes :)

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The part where i should memorise the multiply chart would come in handy

river plank
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Yep

unborn forge
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You know I’m dumb when i can’t even find it

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😀

river plank
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It's all good

unborn forge
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I got it

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LMAO

river plank
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Which numbers?

unborn forge
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20 x 5

river plank
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LETS GO!

unborn forge
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20+5

river plank
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WE WINDOWS

unborn forge
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Windows!!!

river plank
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Okay so now that you find these 2 numbers you split the yellow number to the to the 2 numbers that you found

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like this

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$${\color{red}25}c^2 + {\color{yellow}25}c + {\color{blue}4}={\color{red}25}c^2 + 20c+5c + {\color{blue}4}$$

solar pilotBOT
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TheVinkler

river plank
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Makes sense sor far?

unborn forge
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Mmm

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Yup

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👍

river plank
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Just that it makes since, the magic is yet to happen

unborn forge
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I love this

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Hate math but love this

river plank
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XD

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math is logic, schools just suck at teaching it

unborn forge
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Nah i just suck at logic

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This why i like art

river plank
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Math has a lot of cool things with art but let's discuss that later

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So now I want you to look at this and I want you to look at this as 2 speerate things to factor

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${\color{red}25c^2 + 20c}+{\color{yellow}5c + 4}$

solar pilotBOT
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TheVinkler

river plank
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Now I want you to factor the red side and tell me what you got, and the yellow side and tell me what you got

unborn forge
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Wait what

river plank
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I want you to factor the red side and then the yellow side

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I thought you are american, these guys are good with seperating by color 🙂

unborn forge
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Im canadian😭

river plank
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XD

unborn forge
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VINKLERR

river plank
unborn forge
river plank
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Factor $25c^2+20c$

solar pilotBOT
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TheVinkler

unborn forge
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I can’t

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I’m too dumb😭

river plank
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Why not?

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Relax let's go by it one step at a time

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So first are there any type of factors between 25 and 20?

unborn forge
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For some reason this is really new to me

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Or im brainfarting

river plank
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What is the common factor between 25 and 20?

unborn forge
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Oh

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Greatest common factor?

river plank
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Sure

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Also works

unborn forge
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Thats what theyrecalled for me

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5

river plank
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Great!

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So we can fistr write

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$25c^2+20c=5\cdot5c^2+5\cdot4c=5(5c^2+4c)$

solar pilotBOT
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TheVinkler

river plank
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Now is there anything we can factor from 5c^2 and 4c?

unborn forge
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I don’t like how it’s getting longer lol

river plank
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I am writing all the steps

unborn forge
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Or like one

river plank
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There is one thing we can factor

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remeber that c is just a number

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So we can factor by c

unborn forge
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Oh right

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1c :D

river plank
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$5(5c^2+4c)=5(5c\cdot c+4c)=5c(5c+4)$

solar pilotBOT
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TheVinkler

river plank
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Now is there anthing we can factor form 5c+4?

unborn forge
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No?

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Please no

river plank
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Correct

unborn forge
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LET’S GO

river plank
unborn forge
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No

river plank
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Correct

unborn forge
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:D

river plank
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So after we factored everything from these 2 induvidals

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we get

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${\color{red}5c(5c+4)}+{\color{yellow}5c + 4}$

solar pilotBOT
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TheVinkler

river plank
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Now do you see something intresting?

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Sorry I am trying to type fast and it isn't working

unborn forge
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Lol np

unborn forge
river plank
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LOL

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Ok how about some more coloring

unborn forge
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Also quick random question, what two number times to -81 and adds to -36

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Really bad at finding these

river plank
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$5c({\color{green}5c+4})+{\color{green}5c + 4}$

solar pilotBOT
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TheVinkler

river plank
unborn forge
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??

river plank
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Can you show me the original question? because I feel like you can simplfy it before

river plank
unborn forge
river plank
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NO

unborn forge
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NOOO

river plank
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Hell no

unborn forge
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OH GOD

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Thought i did soemthing

river plank
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remember $(5c+4)^2=(5c+4)(5c+4)$

solar pilotBOT
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TheVinkler

river plank
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$5c({\color{green}5c+4})+{\color{green}5c + 4}=(5c+1)({\color{green}5c + 4})$

river plank
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Now this is the final factored form

unborn forge
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That confused me on so many levels

solar pilotBOT
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TheVinkler

river plank
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Does that make it better?

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I have another idea

unborn forge
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How does it become 5c + 1

river plank
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${\color{yellow}5c}({\color{green}5c+4})+({\color{blue}1})({\color{green}5c + 4})=({\color{yellow}5c}+{\color{blue}1})({\color{green}5c + 4})$

solar pilotBOT
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TheVinkler

river plank
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Does this makes more sense?

unborn forge
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Ohhh

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Its the c

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Gotcha

river plank
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And this is our final form

unborn forge
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Mmm

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So (5c+1) (5c+4)?

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Is the answer

river plank
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yep

unborn forge
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Thats a really explained explanation

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I understand:)

river plank
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Okay

unborn forge
river plank
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Now the way that you write an answer like this is like that

unborn forge
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I meant like well explanation

river plank
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$25c^2 + 25c + 4=25c^2+20c+5c+4=5c(5c+4)+5c+4=(5c+1)(5c+4)$

solar pilotBOT
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TheVinkler

river plank
slate pastureBOT
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@river plank has given 1 rep to @unborn forge

unborn forge
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Yooo

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Ty

river plank
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np

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no idea what those mean

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So you got the idea?

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kinda?

unborn forge
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Yeah 👍

river plank
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Okay try another one when you get stuck let me know, mention me so I would notice

unborn forge
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Not sure if the teachers gonna be okay with me writing a college looking answer in a grade 10 exam

river plank
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It's not college looking

unborn forge
river plank
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LETS GO

unborn forge
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Yayyy

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I do need to study tho

river plank
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Okay try this one because there is a trick

unborn forge
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But its 12 am😭😭😭

river plank
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XD

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been there multple times

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$x^2+5x-6$

solar pilotBOT
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TheVinkler

unborn forge
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That doesnt look

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Bad…

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Thats what concerns me

river plank
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it isn't that bad

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LOL

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don't be afraid it almost doesn't bite

unborn forge
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ALMOST?

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😨

river plank
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Just solve it, it isn't that bad

unborn forge
river plank
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Yep

unborn forge
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6 and -1

river plank
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okay

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keep going

unborn forge
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Uh

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Okay okay so

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I had to scroll up so i know what the formatting was

river plank
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Okay, keep going

unborn forge
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$x^2+6x-1x-6$

solar pilotBOT
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𝓚𝓾𝓻𝓲

unborn forge
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Righttt

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?

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Wait lmao

river plank
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Oh I didn't know you were going to use latex

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gj

unborn forge
river plank
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XD

unborn forge
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Right thoc

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?

river plank
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So far yes

unborn forge
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And then like

river plank
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cmon u can do it!

unborn forge
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AHHH

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Split the question is two halves

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Factor x^2 + 6x

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And uh

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1x rightttt

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And the other one, x - 6 we do nothin

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$(x+6)(x-6)$

river plank
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No you juped

solar pilotBOT
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𝓚𝓾𝓻𝓲

river plank
unborn forge
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Dang it

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Is it not just 1?

river plank
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here we had

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$x(x+6)-x-6$

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right?

unborn forge
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Mhm

solar pilotBOT
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TheVinkler

river plank
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mb

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-6

unborn forge
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Lol

river plank
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XD

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So from here

unborn forge
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Oh no the -

river plank
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LOL

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so we get

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$x(x+6)-(x+6)$

solar pilotBOT
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TheVinkler

unborn forge
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Yes

river plank
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which we factor and get?

unborn forge
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Wait

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What

river plank
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I factored -1

unborn forge
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Yeah

river plank
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$-x-6=-(x+6)$

solar pilotBOT
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TheVinkler

river plank
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So now we factor and get?

unborn forge
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WHAT

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hold on let me brain

unborn forge
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Okay uh

unborn forge
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Are you asking me to factor it

river plank
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$x(x+6)-(x+6)$

solar pilotBOT
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TheVinkler

river plank
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factor this

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get the final answer

unborn forge
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Oh

river plank
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Cmon you can do this

unborn forge
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Im just confused how it became positive

river plank
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the +6?

unborn forge
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Yeah

river plank
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If you factor the -1 from -x-6 you get -(x+6)

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$-(x+6)=-x-6$

solar pilotBOT
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TheVinkler

unborn forge
river plank
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yep

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just think about it

unborn forge
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Yeah bevause its one

river plank
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$-x-6=(-1)x+(-1)6=-1(x+6)=-(x+6)$

solar pilotBOT
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TheVinkler

river plank
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$x(x+6)-(x+6)$ So factor this

solar pilotBOT
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TheVinkler

unborn forge
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Hmm

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I dont got this lol

river plank
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what do you mean this?

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be specific

unborn forge
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No you were saying i got this as encouragement

river plank
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LOL

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Just factor this

river plank
unborn forge
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Dont you jusy gottafactor the right side?

river plank
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we just did

unborn forge
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Can you say it?

river plank
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$-x-6=-(x+6)$

unborn forge
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I might understand if its like

solar pilotBOT
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TheVinkler

unborn forge
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Connected

river plank
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$x(x+6)-(x+6)$

solar pilotBOT
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TheVinkler

unborn forge
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Okay

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I get itish now

river plank
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So the answer is?

unborn forge
river plank
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nope

unborn forge
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Dudeeee rhis actually hurts

river plank
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You can still factor it

unborn forge
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By a number or just x

river plank
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$x{\color{red}(x+6)}-{\color{red}(x+6)}$

solar pilotBOT
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TheVinkler

unborn forge
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Oh god not this again

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Let me scroll up

river plank
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If you don't get it now I will come to Canada!

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DUDE

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STOP SCROLLING UP

unborn forge
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I need past reference 😔

river plank
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$xu-u$

solar pilotBOT
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TheVinkler

river plank
#

factor this?

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ok?

unborn forge
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I love tiu for dealing with me

river plank
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XD np

unborn forge
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Is it not just x???

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Oh gosh

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Its not

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Hagebrndj

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I looked up

unborn forge
river plank
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LETS GO

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finally

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good job

unborn forge
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Lmaooo

river plank
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LOL

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practice those kind of questions you will get the hang of it evantully

unborn forge
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Eventually 😔

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The exam is tomorrow

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😊

river plank
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LOL

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then next time practice for it in advance

unborn forge
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Yeah…