# Homework Help: Absolute value question

1. Jan 5, 2008

### Quinn Morris

1. The problem statement, all variables and given/known data

25|x| = x^2 + 144

2. Relevant equations

none

3. 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.....

2. Jan 5, 2008

### 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.

3. Jan 5, 2008

### Quinn Morris

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

4. Jan 5, 2008

### Gib Z

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

5. Jan 5, 2008

k thx