Answer
$\left\{\pm3, \pm 3i\right\}$
Work Step by Step
Recall the definition of absolute value:
$|x|=a \longrightarrow x=a \text{ or } x=-a$
Thus,
$|x^2|=9\longrightarrow x^2=9 \text{ or } x^2 = -9$
Solving each equation gives:
\begin{align*}
x^2&=9 &\text{ or}& &x^2=-9\\
\sqrt{x^2}&=\pm\sqrt9 &\text{or}& &\sqrt{x^2}=\pm\sqrt{-9}\\
x&=\pm3 &\text{or}& &x=\pm3i
\end{align*}
So, our answers are: $x=\pm3$ or $x=\pm3i$
