Quadratic Equation Question | Mathematics | Page 1

trail rapids Mar 31, 2023, 1:48 AM

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If two consecutive integers are multiplied, the product is 4 more than four times the sum of these 2 integers. What are the two integers?

hexed steepleBOT Mar 31, 2023, 1:48 AM

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trail rapids If two consecutive integers are multiplied, the product is 4 more than four time...

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Wait patiently for a helper to come along.
Once someone helps you, say thank you and close the thread with: ```diff
+close

wide dawn Mar 31, 2023, 2:00 AM

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trail rapids If two consecutive integers are multiplied, the product is 4 more than four time...

Since the integers are quadratic, let them be x and x+1

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Since the product of the integers is 4 times the sum of the integers

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x(x+1)=4(x+(x+1))

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Solve for x

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Boom

trail rapids Mar 31, 2023, 2:01 AM

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I got that formula down

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What do you do from there

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Wair actually

wide dawn Mar 31, 2023, 2:02 AM

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solve for x?

trail rapids Mar 31, 2023, 2:02 AM

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One second

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I think I might have just made a stupid mistake

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Let me redo what I did

wide dawn Mar 31, 2023, 2:04 AM

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Sure

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If it's still wrong tell me

trail rapids Mar 31, 2023, 2:05 AM

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wide dawn If it's still wrong tell me

Yeah its still wrong

wide dawn Mar 31, 2023, 2:05 AM

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Okay let's solve this together

trail rapids Mar 31, 2023, 2:05 AM

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Ignore the crossed out stuff

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What am I doing wrong

wide dawn Mar 31, 2023, 2:06 AM

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Wait lemme check

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See so

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The LHS is

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$x^2+x$

prisma lakeBOT Mar 31, 2023, 2:06 AM

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Zrekon

wide dawn Mar 31, 2023, 2:07 AM

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RHS is

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$8x+4$

prisma lakeBOT Mar 31, 2023, 2:07 AM

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Zrekon

wide dawn Mar 31, 2023, 2:07 AM

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$x^2+x=8x+4$

prisma lakeBOT Mar 31, 2023, 2:07 AM

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Zrekon

wide dawn Mar 31, 2023, 2:07 AM

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Right?

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hh

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Ahh

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I see your mistake

trail rapids Mar 31, 2023, 2:08 AM

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What is it

wide dawn Mar 31, 2023, 2:08 AM

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See how you've solved the quadratic equation using the quadratic formulae?

trail rapids Mar 31, 2023, 2:08 AM

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Yeah

wide dawn Mar 31, 2023, 2:08 AM

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Check it again

trail rapids Mar 31, 2023, 2:09 AM

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I cant find the error

wide dawn Mar 31, 2023, 2:10 AM

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$\frac{-b+_-\sqrt{b^2-4ac}}{2a}$

prisma lakeBOT Mar 31, 2023, 2:10 AM

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Zrekon

wide dawn Mar 31, 2023, 2:10 AM

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Now check the square root

trail rapids Mar 31, 2023, 2:10 AM

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K

wide dawn Mar 31, 2023, 2:10 AM

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In your solution, check the square root

trail rapids Mar 31, 2023, 2:11 AM

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Is it positive 49

wide dawn Mar 31, 2023, 2:11 AM

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Yes!

trail rapids Mar 31, 2023, 2:11 AM

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Damn

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It was such a simple mistake

wide dawn Mar 31, 2023, 2:11 AM

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It'll be (-7)^2, which makes it positive!

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Don't worry we've all been there

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Now fix it

trail rapids Mar 31, 2023, 2:12 AM

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I fixed it

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What do I do next

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I know the correct answer and the quadratic equation isnt giving me it

wide dawn Mar 31, 2023, 2:12 AM

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Is it 10?

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The answer?

trail rapids Mar 31, 2023, 2:12 AM

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Its 8 and 9

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Apparently

wide dawn Mar 31, 2023, 2:13 AM

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Okay

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That's interesting

trail rapids Mar 31, 2023, 2:13 AM

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Yeah

wide dawn Mar 31, 2023, 2:13 AM

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Ah oka

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It's 8 and 9

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See I did a dumb mistake myself

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It happens

trail rapids Mar 31, 2023, 2:13 AM

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Is there another mistake in my work

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Oh

wide dawn Mar 31, 2023, 2:13 AM

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No it's correct

trail rapids Mar 31, 2023, 2:13 AM

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What happened

wide dawn Mar 31, 2023, 2:13 AM

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just solve the equation

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Add (49+16)

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What do you get

trail rapids Mar 31, 2023, 2:14 AM

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65

wide dawn Mar 31, 2023, 2:14 AM

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Add it again

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No

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wait

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Bruh

trail rapids Mar 31, 2023, 2:14 AM

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What

wide dawn Mar 31, 2023, 2:14 AM

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It's

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Wow

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I'm dumb

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See

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It's 4ac

trail rapids Mar 31, 2023, 2:15 AM

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Yeah

wide dawn Mar 31, 2023, 2:15 AM

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4(1)(4)

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16

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Exactly

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Wait

trail rapids Mar 31, 2023, 2:15 AM

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What

wide dawn Mar 31, 2023, 2:15 AM

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Lemme just solve it

trail rapids Mar 31, 2023, 2:15 AM

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Yeah

wide dawn Mar 31, 2023, 2:16 AM

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despair despair

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I need to practise

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Sorry for wasting so much of your time man

trail rapids Mar 31, 2023, 2:16 AM

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Wait

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I realized our error

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I read the question wrong

wide dawn Mar 31, 2023, 2:17 AM

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Ye

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It's 4 more than 4 times the sum

trail rapids Mar 31, 2023, 2:17 AM

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The equation is missing a +4

wide dawn Mar 31, 2023, 2:17 AM

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So

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Ye

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Exactly

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I'm just so dumb

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Sorry

trail rapids Mar 31, 2023, 2:17 AM

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Nah

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Let me retry it now

wide dawn Mar 31, 2023, 2:18 AM

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$x^2+x=4+8x+4$

prisma lakeBOT Mar 31, 2023, 2:18 AM

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Zrekon

wide dawn Mar 31, 2023, 2:18 AM

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$x^2+x=8x+8$

prisma lakeBOT Mar 31, 2023, 2:18 AM

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Zrekon

trail rapids Mar 31, 2023, 2:18 AM

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Yeah I get 8 now

wide dawn Mar 31, 2023, 2:19 AM

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Yeah

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good

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Im stupid

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Sorry for wasting your time

trail rapids Mar 31, 2023, 2:19 AM

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Nah

wide dawn Mar 31, 2023, 2:19 AM

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mann

trail rapids Mar 31, 2023, 2:19 AM

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Its all good

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U helped me realize my mistake

wide dawn Mar 31, 2023, 2:19 AM

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And you helped me realise mine

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lol

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okay then

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Anything else?

trail rapids Mar 31, 2023, 2:20 AM

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Maybe

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I have like 2 more problems left

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Ill try solving them myself

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If I need help ill come back here

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Im pretty sure ill need help tho

wide dawn Mar 31, 2023, 2:20 AM

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hm

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I'll be here then

trail rapids Mar 31, 2023, 2:20 AM

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Ty

wide dawn Mar 31, 2023, 2:25 AM

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Need any help?

trail rapids Mar 31, 2023, 2:35 AM

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wide dawn Need any help?

Yeah

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You still here?

wide dawn Mar 31, 2023, 2:36 AM

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Yes

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Send

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Tell question

trail rapids Mar 31, 2023, 2:36 AM

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#

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Heres my work

wide dawn Mar 31, 2023, 2:38 AM

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Okay

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Wait

trail rapids Mar 31, 2023, 2:38 AM

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Answer should be 3

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Idk how to get there tho

wide dawn Mar 31, 2023, 2:39 AM

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Yes wait

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uh

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Okay

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See the figure

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Just the outer figure

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Cut it out into 4 rectangles of width w each, one of length 16 and the other of length 12

trail rapids Mar 31, 2023, 2:40 AM

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Okay

wide dawn Mar 31, 2023, 2:41 AM

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Something like this

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trail rapids Mar 31, 2023, 2:41 AM

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Yeah

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Ik the area of the w equals like 93

wide dawn Mar 31, 2023, 2:41 AM

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?

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Area of the width?

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Wtf is that

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The width has an area?

trail rapids Mar 31, 2023, 2:42 AM

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I mean like the outer part they added

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Has an area of 93

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The pathway

wide dawn Mar 31, 2023, 2:42 AM

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ah okay

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Yea okay

trail rapids Mar 31, 2023, 2:43 AM

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What equation do i use to solve this

wide dawn Mar 31, 2023, 2:43 AM

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Ye

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See find the area of the rectangles seperately

trail rapids Mar 31, 2023, 2:43 AM

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Yeah

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One of them is 192

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Other is 93

wide dawn Mar 31, 2023, 2:44 AM

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Not that

trail rapids Mar 31, 2023, 2:44 AM

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Oh

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U mean like cut up the outer part into rectangles?

wide dawn Mar 31, 2023, 2:44 AM

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Wait

trail rapids Mar 31, 2023, 2:44 AM

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K

wide dawn Mar 31, 2023, 2:45 AM

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Ye

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These highlighted parts

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trail rapids Mar 31, 2023, 2:46 AM

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How tf do that

wide dawn Mar 31, 2023, 2:46 AM

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See

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The length of the red part is

trail rapids Mar 31, 2023, 2:46 AM

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16 + 2w

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Oh

wide dawn Mar 31, 2023, 2:46 AM

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Ye

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16+2w

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Dumb me

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Ye

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And width is w

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So area is?

trail rapids Mar 31, 2023, 2:47 AM

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(16+2w)(w) so

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16w+2w^2

wide dawn Mar 31, 2023, 2:47 AM

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Don't solve it yet

trail rapids Mar 31, 2023, 2:47 AM

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Oh

wide dawn Mar 31, 2023, 2:48 AM

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Let's keep it( 16+2w)(w)

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For now

trail rapids Mar 31, 2023, 2:48 AM

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K

wide dawn Mar 31, 2023, 2:48 AM

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Just for simplification

trail rapids Mar 31, 2023, 2:48 AM

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Then do we double it

wide dawn Mar 31, 2023, 2:48 AM

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Now find the area of the blue part

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Exactly

trail rapids Mar 31, 2023, 2:48 AM

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K

wide dawn Mar 31, 2023, 2:48 AM

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We're going to double it

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First find the area of the blue part

trail rapids Mar 31, 2023, 2:48 AM

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(12+2w)(w)

wide dawn Mar 31, 2023, 2:49 AM

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see

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That's wrong

trail rapids Mar 31, 2023, 2:49 AM

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Oh

wide dawn Mar 31, 2023, 2:49 AM

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See the blue rectangle doesn't cover the whole area

trail rapids Mar 31, 2023, 2:49 AM

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What is it

wide dawn Mar 31, 2023, 2:49 AM

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It's taken by the red one

trail rapids Mar 31, 2023, 2:49 AM

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Yeah

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I see

wide dawn Mar 31, 2023, 2:49 AM

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It'll be 12w

trail rapids Mar 31, 2023, 2:49 AM

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12w

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Yeah

wide dawn Mar 31, 2023, 2:50 AM

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Now double it

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24w

trail rapids Mar 31, 2023, 2:50 AM

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24w

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And the other one is

wide dawn Mar 31, 2023, 2:50 AM

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And the area of the red part?

trail rapids Mar 31, 2023, 2:50 AM

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32w+4w^2?

wide dawn Mar 31, 2023, 2:50 AM

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Yep

trail rapids Mar 31, 2023, 2:50 AM

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Then do we add them

wide dawn Mar 31, 2023, 2:51 AM

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Yes!

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You're getting it

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We add them and keep them equal to?

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Think what they're equal to

trail rapids Mar 31, 2023, 2:51 AM

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44w+4w^2?

wide dawn Mar 31, 2023, 2:51 AM

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Wha

trail rapids Mar 31, 2023, 2:52 AM

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Nvm

wide dawn Mar 31, 2023, 2:52 AM

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32w+4w^2+24w

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Add

trail rapids Mar 31, 2023, 2:52 AM

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Yeah i added 12 for some reason

wide dawn Mar 31, 2023, 2:52 AM

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Hm

trail rapids Mar 31, 2023, 2:52 AM

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Its 56w

wide dawn Mar 31, 2023, 2:52 AM

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Yes

trail rapids Mar 31, 2023, 2:52 AM

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Not 44

wide dawn Mar 31, 2023, 2:52 AM

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56w+4w^2

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Now what is this sum equal to

trail rapids Mar 31, 2023, 2:52 AM

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Yeah

wide dawn Mar 31, 2023, 2:52 AM

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Think

trail rapids Mar 31, 2023, 2:53 AM

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It equals

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Hmm

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Idk

wide dawn Mar 31, 2023, 2:53 AM

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See

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The area we found is the area of the red and blue part

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The total area of the pathway

trail rapids Mar 31, 2023, 2:53 AM

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Oh yeah

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Whats w tho

wide dawn Mar 31, 2023, 2:53 AM

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Earlier you found out the area of the pathway, remember?

trail rapids Mar 31, 2023, 2:53 AM

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Yeah

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93

wide dawn Mar 31, 2023, 2:54 AM

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What was it?

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That's it!

trail rapids Mar 31, 2023, 2:54 AM

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Let me enter this

wide dawn Mar 31, 2023, 2:54 AM

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56w+4w^2=93

trail rapids Mar 31, 2023, 2:54 AM

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In the quadratic formula

wide dawn Mar 31, 2023, 2:54 AM

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Ye

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Solve and tell

trail rapids Mar 31, 2023, 2:54 AM

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K

wide dawn Mar 31, 2023, 2:54 AM

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Something feels funny

trail rapids Mar 31, 2023, 2:55 AM

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Wait

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Its the exact same as last time

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It gets a negative answer

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With a bunch of decimals

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Not 3

wide dawn Mar 31, 2023, 2:55 AM

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Wha

trail rapids Mar 31, 2023, 2:55 AM

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Am i entering it correct

wide dawn Mar 31, 2023, 2:56 AM

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Wait a sec

trail rapids Mar 31, 2023, 2:56 AM

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K

wide dawn Mar 31, 2023, 2:57 AM

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Let me

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Do it myself

trail rapids Mar 31, 2023, 2:57 AM

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K

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What did u get

wide dawn Mar 31, 2023, 3:00 AM

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,w 4w^2+56w-93

prisma lakeBOT Mar 31, 2023, 3:00 AM

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Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

wide dawn Mar 31, 2023, 3:00 AM

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Okay

trail rapids Mar 31, 2023, 3:01 AM

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Is that right?

wide dawn Mar 31, 2023, 3:02 AM

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Something's not right

trail rapids Mar 31, 2023, 3:02 AM

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Yeah

wide dawn Mar 31, 2023, 3:02 AM

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Either I'm just plain dumb

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Or the questions wrong or something

trail rapids Mar 31, 2023, 3:02 AM

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Maybe thats the answer

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I dont think 3 is the correct answer

wide dawn Mar 31, 2023, 3:03 AM

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Ye

trail rapids Mar 31, 2023, 3:03 AM

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I asked me friend for the answer and he said 3

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He might be wrong

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Probably is

wide dawn Mar 31, 2023, 3:03 AM

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Interesting

trail rapids Mar 31, 2023, 3:03 AM

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Also

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To get 3/2

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Nvm

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Nvm

wide dawn Mar 31, 2023, 3:05 AM

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Yeah

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It's 3/2

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100%

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It can't be 3

trail rapids Mar 31, 2023, 3:05 AM

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But like

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If u solve the equation with 3

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It gets the answer

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When i plug in 3/2

wide dawn Mar 31, 2023, 3:05 AM

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No it doesn't

trail rapids Mar 31, 2023, 3:05 AM

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I sont get 285

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Wait shit

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Its 2w

wide dawn Mar 31, 2023, 3:06 AM

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In what equation

trail rapids Mar 31, 2023, 3:06 AM

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3 divided by 2

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Is 1.5

wide dawn Mar 31, 2023, 3:06 AM

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In what equation you plugging it?

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It's 3/2

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Your friend is wrong

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Tell him

trail rapids Mar 31, 2023, 3:07 AM

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Tysm

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Yeah i did lmao

trail rapids Mar 31, 2023, 3:08 AM

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wide dawn In what equation you plugging it?

(16+2w)(12+2w)

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I forgot to multiply 1.5 by 2

wide dawn Mar 31, 2023, 3:08 AM

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Hm

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It'll be 3/2

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Confirm from somewhere

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It'll be 3/2

#Quadratic Equation Question