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# Mathcounts oh no!

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What is the value of r for which $$(r-5)^2=(r+2)^2$$?

Joke: Does MATHCOUNTS or does math count?

Sorry....

ANYWAY ON TO THE WORK, I HAVE:

$$r^2 - 10r + 25=r^2+4r+4$$

Then...

Uhmm...

Idk...

Could somebody help me out?

EDIT::

Nvm, solved it!!!

Heres what I got after my first step:

$$r^2 - 10r + 25=r^2+4r+4$$

(subtracted r^2 from both sides)

$$21=14r$$

(like terms to their sides)

$$r=\frac{21}{14}$$

(Simplify)

Could somebody check my work?

Nov 12, 2019
edited by tommarvoloriddle  Nov 12, 2019
edited by tommarvoloriddle  Nov 12, 2019
edited by tommarvoloriddle  Nov 12, 2019
edited by tommarvoloriddle  Nov 12, 2019
edited by tommarvoloriddle  Nov 12, 2019

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Hi Tom...riddle

The best way to check question like this is to use Desmos to graph it

Graph

$$y=x^2-10x+25\\ and \\ y=x^2+2x+4\\$$

The x value of where the 2 graphs cross will give the answer

And here is the graph

https://www.desmos.com/calculator/zl5tvz0rp0

Nov 12, 2019
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GENIUS

tommarvoloriddle  Nov 12, 2019
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r^2 + 2r +4    ?     You need to investigate that part !

Another way to check your work.....Just put your solution into the eqation and see if it works....

Nov 12, 2019
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Sorry, I thought I put -2r....

I'll fix that.

Anything else?

tommarvoloriddle  Nov 12, 2019
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It should be :   r^2 + 4r + 4

ElectricPavlov  Nov 12, 2019
edited by ElectricPavlov  Nov 12, 2019
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Oh shoot-

When you do math at 3:00 am your time

tommarvoloriddle  Nov 12, 2019
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Thanks for picking that up EP

Sorry Tom...riddle  about the transfer error.

It was super bad luck that your errror and my different error alligned to give the same answer.

If it hadn't I would have checked both our work to see where the error lay.

Still my checking method is still sound.

Melody  Nov 12, 2019
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Agreed-Its my mistake coupled with yours....

tommarvoloriddle  Nov 12, 2019
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(r - 5)^2  = (r + 2)^2

r^2 - 10 r + 25  =  r^2 + 4r + 4

-10r + 25  = 4r + 4

-14r  =  -21

r = -21/-14 =   3 / 2  = 1.5

Nov 12, 2019