Answer
$x=\left\{ -9i,9i \right\}$
Work Step by Step
Taking the square root of both sides, the solutions to the given equation, $
x^2=-81
,$ are
\begin{array}{l}\require{cancel}
x=\pm\sqrt{-81}
\\\\
x=\pm\sqrt{-1}\cdot\sqrt{81}
\\\\
x=\pm i\cdot\sqrt{(9)^2}
\\\\
x=\pm i\cdot9
\\\\
x=\pm9i
.\end{array}
Hence, the solution is $
x=\left\{ -9i,9i \right\}
.$
