Here is the equation: |x|^2 + 2|x| -3=0
The answer is + or - one. I solved it normally disregarding the abs. value and I got 1 and -3.
Let $\displaystyle \displaystyle X = |x|$ so that your equation becomes $\displaystyle \displaystyle X^2 + 2X - 3 = 0$.
Solve for $\displaystyle \displaystyle X$ and then use that solution to solve for $\displaystyle \displaystyle |x|$.