Answer
The solution set is $\color{blue}{\left\{-3i, 3i\right\}}$.
Work Step by Step
Take the square root of both sides:
$\sqrt{x^2} = \pm \sqrt{-9}
\\x=\pm \sqrt{-9}
\\x=\pm \sqrt{9(-1)}
\\x=\pm \sqrt{3^2(-1)}
\\x=\pm 3\sqrt{-1}$
Note that $\sqrt{-1} = i$.
Thus, the equation above simplifies to:
$x=\pm 3i$
Therefore, the solution set is $\color{blue}{\left\{-3i, 3i\right\}}$.