# Thread: I can't see how they solve this equation!

1. ## I can't see how they solve this equation!

This is one line in an optimization problem…

x2[3600+(200-x)2 ] = (200-x)2(8100+x2)

According to the book it should equal…

3600x2 = 8100(200-x)2

I can’t see how!

2. Originally Posted by NFZ17
This is one line in an optimization problem…

x2[3600+(200-x)2 ] = (200-x)2(8100+x2)

According to the book it should equal…

3600x2 = 8100(200-x)2

I can’t see how!
Is it
$\displaystyle x^2[3600+(200-x)^2]=(200-x)^2(8100+x^2)$
??

3. Yeah that's it, sorry I copied and pasted from a word doc!!

4. Originally Posted by NFZ17
This is one line in an optimization problem…

x2[3600+(200-x)2 ] = (200-x)2(8100+x2)

According to the book it should equal…

3600x2 = 8100(200-x)2

I can’t see how!
$\displaystyle x^2[3600+(200-x)^2]=(200-x)^2(8100+x^2)$

Multiplying these out, we get...

$\displaystyle 3600x^2+x^2(200-x)^2=8100(200-x)^2+x^2(200-x)^2$

therefore, since $\displaystyle x^2(200-x)^2$ is common to both sides..

$\displaystyle 3600x^2=8100(200-x)^2$

5. Thanks a million! totally missed that!