**Question**

How many integer solutions exist for the equation x

^{2}– 8|x| – 48 =0?

**Explanation**

One approach is to solve when x > 0 and then solve for x < 0. However, there is a slightly simpler method.

Note that x

^{2}is the same as |x|^{2}, so we can treat the equation as a quadratic in |x|.Or, |x|

^{2 }– 8|x| – 48 = 0(|x| – 12|) (|x| + 4) = 0

|x| could be 12. |x| cannot be -4.

If |x| could be 12, x can be -12 and 12.

Two possible solutions exist.