How do I solve a quadratic equation with absolute value?

[Quinn Morris]

Homework Statement

25|x| = x^2 + 144

Homework Equations

none

The Attempt at a Solution

okay well, I'm not quite sure what to do, do i try to isolate the |x|? and then break it up into a postive and negative?

|x| = (x^2 + 144)/25 ?

but from here i become lost...

 

[HallsofIvy]

Why not do what you just said? You have "isolated" |x|, now break it into positive and negative parts.

If $x\ge 0$ then |x|= x so the equation becomes $x= (x^2+ 144)/25$ or $25x= x^2+ 144$. Solve that quadratic equation. Remember that only $x\ge 0$ are valid solutions.

If x< 0, then |x|= -x so the equation becomes $-x= (x^2+ 144)/25$ or $-25x= x^2+ 144$. Solve that quadratic equation. Remember that only x< 0 are valid solutions.

You might notice that it is easier to first break into two cases and then solve for x.

 

[Quinn Morris]

okay so should my answer be x = +/- 16, +/- 9?

 

[Gib Z]

okay so should my answer be x = +/- 16, +/- 9?

It's quite easy to check yourself =P Especially when checking one of the positive solutions gets rid of the negative counterpart as well.

 

[Quinn Morris]

k thx