Solving QUADRATIC Equations

[pale jewel]

I have a attached picture

[pale jewel]

I have a upcoming exam, however my teacher says I have to use this method, when I've never seen it before...

So i can't change it to ac²xbcxc method if it's correct... I'm just looking for some tutorial of this method

[potent timber]

look for "completing the square" method

[swift reef]

This is a Quadratic Expression, not a Quadratic Equation.
May you post the "exact" question "as is"?

[pale jewel]

The "exact" question is 2x² + 5x + 3 = 0

[pale jewel]

I had a quick look at the method, it looks to be the right one, but I'll have a look when I got some time

[scenic siren]

This looks like factoring to me

Not completing the square

[pale jewel]

However, doing some independent work, I found the normal formula was easier, but the teacher has done another method without actually explaining

[scenic siren]

Basically for a quadratic of the form ax^2+bx+c where a = 0 it can be factored as (x+d)(x+e) where d + e = b and d*e = c

[pale jewel]

Yes I found that method very easy, but I am going to practice the "completing the square", even though it doesn't make sense to me

[scenic siren]

Why doesn’t it make sense?

Understanding something will always make you better at it then simply memorizing and repetition

[pale jewel]

I don't think I understand the formula

[scenic siren]

The “formula” for completing the square is just the quadratic formula

Do you mean the steps?

[pale jewel]

Ok here

I did the equation of a different question and understand it very well

[scenic siren]

Yep that’s the quadratic formula

[pale jewel]

It's kind of hard explaining, but to make it easier, I would say I don't understand the formula yet, as I haven't had a tutorial, the teacher told us to write it down but didn't show us, and this is the first time I've done quadratics

[potent timber]

the root is wrong

you should have sqrt(25)=5

[scenic siren]

Just the 5th step from the bottom

[potent timber]

not sqrt(25)=sqrt(5)

[potent timber]

indeed

[scenic siren]

The quadratic formula is the generalization of completing the square

If you want to understand the quadratic formula, you should first learn how to complete the square

Do you know how to?

[pale jewel]

No

It's my first time doing it

[pale jewel]

What is sqrt?

[potent timber]

square root

[scenic siren]

By the way this is wrong

It should be (x+3/2)(x+1)

[scenic siren]

Your teacher didn’t teach you how?

And they expect you to use it on a test?

[pale jewel]

He taught us like 10 different algebra, then logarithms and solving simultaneous equations and some it it's just alot to remember

[scenic siren]

So he did teach you how to complete the square but you don’t remember…

[potent timber]

It seems you need to practice more

[pale jewel]

He never showed us the formula

[potent timber]

in order to remember

[potent timber]

hmmm

[scenic siren]

Completing the square is not a formula, but a method

Just like combination/elimination and substitution in simultaneous equations

Or like using inverse operations to solve linear equations

[pale jewel]

He wrote that method on the board as its the "easiest"

[scenic siren]

If you don’t know how to, I suggest watching a YouTube tutorial

Such as khan academy

[scenic siren]

Easiest is subjective

It really depends on the coefficients of the quadratic

[pale jewel]

Coefficient is the numbers?

[scenic siren]

However, the key thing about completing the square it is always works for every quadratic

[scenic siren]

Yes

When all else fails such as factoring or square roots, completing the square is the last but most reliable method

The quadratic formula essentially already “completed” the square for you based of the coefficients and isolated x

That’s also why the quadratic formula always works

[pale jewel]

But I didn't do it right lol

I will definitely do some more practice and have a look at khan academy but I think it is time for bed

And I'll have a look at the fifth line, however the answer is correct as it says on the answer sheet the teacher gave us

[scenic siren]

Yes you did, you just made a tiny error in writing a line

But it didn’t affect your solution anyway

[pale jewel]

If U see I write those boxes to basically highlight what I did as it makes me understand if U get it, but I must have made a mistake in the root itself?

So the boxes is what I'm going to change in the next line

[scenic siren]

You turned sqrt(25) into sqrt(5) for one line but then changed it to 5, which is correct

So even though you made a mistake you i guess subconsciously corrected it

[pale jewel]

Oh Ur think of solving quadratics in the form of the ax²... I'm solving non monic quadratic equations

Yes because √25 is 5

[scenic siren]

That looks like a quadratic to me…

[pale jewel]

It is but in non monic

[scenic siren]

Well, you divided out a so it is of the form where the leading coefficient is a

So the method works

[pale jewel]

Oh i see, I wrote the root on top of the 5 🤦

[scenic siren]

Yep

[pale jewel]

Here I'll show U the sheet I'm working off

So these are all the types of quadratics I that will be in the exam

The hard thing is he gave us the "completing the square method" but showed us the quadratic formula which also doesn't help, but I found it thx to Nilson

[scenic siren]

I see no completing the square on the review sheet

[pale jewel]

Yes but he showed us the completing the square method

And he doesn't want me to change the method, so I can't really do the quadratic formula that I understand more, so I have to do the practice tomorrow for the completing the square

[scenic siren]

Does he require it on the test though

[pale jewel]

I also got given another formula sheet but that has more different quadratic equations, where U have to expand and just more, than full answer questions, them I get given my logarithms sheet and maybe solving inequalities

[pale jewel]

I was going to ask that question today but he was sick and won't be here tomorrow 😩

Well it was a good chat, thanks for the help, I'll send a few messages of showing my working for completing the square and if it's wrong just send some feedback or whatever 👍

[scenic siren]

Sorry

I was gone for a second

[scenic siren]

Don’t mindlessly work

Search up a tutorial

Watch videos until you understand it

If you have trouble understanding it just ask

[pale jewel]

No no, Ur fine man... I got to get to bed

[pale jewel]

Ok I can sure do that, I'll have to send an email if I need it on the exam, even though he told me not to change but I'll still study it

[scenic siren]

Okay

Good luck

[swift reef]

Okay... this is a Quadratic Equation (because of the equal sign)
Without the equal sign (as you posted it initially), it is a Quadratic Expression.
Would you like me to do the question using Completing the Square method, show all work, and answer any question you may have; or would you like to attempt it first, post your solution and wait for feedback?

[pale wren]

alright, based of the sheet you showed me

i think i can do it

2x^2 + 5x + 3 = 0

one is that you seperate 5x into 2x + 3x (because 2 + 3 = 5 and 2 * 3 = 6 (which is a * c)) as your sheet says

2 is that you can try to complete the squares by multiplying the LHS and RHS by 2

so that it's easier to complete

4x^2 + 10x + 6 = 0

so you can rewrite 4x^2 as (2x)^2 and 10x as 2.2x.5/2

the reason i multiply by 2 here is that i want to turn 2x^2 into 4x^2 so that it can be a square thing, and also remove the roots

[pale jewel]

I would like to attempt it first and show my working, but I'll watch a few videos before I do this afternoon

Ok the question is 2x² - 3x -2 = 0
Using the quadratic formula
a=2, b=-3 and c=-2
So -(-3)± √(-3)²-4 ×2 ×(-2)

                2x2

So it would be 3± 25
-------
4
Now it's √25=5

So 3+5
---- =2
4.

So thats x²

And 3-5
---
4
Is -1/2?

So x¹=-1/2 then x²=2

[pale jewel]

This must be completing the square method because I don't understand the 3x and how it goes to 6

[pale wren]

no... it isn't

[pale wren]

this is one of the most famous methods to factorize a quadratic

for a quadratic $ax^2 + bx + c$

[fleet quail]

1 divided by 0 equals Infinity

[pale wren]

you want to try to find 2 numbers $b_1$ and $b_2$ such that $b_1 + b_2 = b$ and $b_1b_2 = ac$

[fleet quail]

1 divided by 0 equals Infinity

[pale wren]

in your case, for the equation $2x^2 + 5x + 3$, you can get $2\cdot3 = 6$ (which is $ac$), and seperate the $5x$ into $2x + 3x$, because those 2 numbers timesing together to get $6$

[fleet quail]

1 divided by 0 equals Infinity

[pale wren]

@pale jewel https://www.youtube.com/watch?v=s5t0a2LV37M

[pale jewel]

But it is not an expression

It's a equation

And I have to solve for X, not factorize

I have to solve for X using the quadratic formula

[pale wren]

well

to solve

one of the ways to solve equations is to factorize

so for your $2x^2 + 5x + 3 = 0$

[fleet quail]

1 divided by 0 equals Infinity

[pale wren]

then $2x^2 + 2x + 3x + 3 = 0$

[fleet quail]

1 divided by 0 equals Infinity

[pale wren]

$2x(x + 1) + 3(x + 1) = 0$

[fleet quail]

1 divided by 0 equals Infinity

[pale wren]

$(2x + 3)(x + 1) = 0$

[fleet quail]

1 divided by 0 equals Infinity

[pale wren]

so since the product is equal to zero

then $2x + 3$ or $x + 1$ must be equal to zero

[fleet quail]

1 divided by 0 equals Infinity