Answer
$x=\left\{ 3-3i,3+3i \right\}$
Work Step by Step
Taking the square root of both sides (the Square Root Property) and using $i=\sqrt{-1}$, the solutions to the given equation, $
(x-3)^2=-9
,$ are
\begin{array}{l}\require{cancel}
x-3=\pm\sqrt{-9}
\\\\
x-3=\pm\sqrt{-1}\cdot\sqrt{9}
\\\\
x-3=\pm i\cdot\sqrt{(3)^2}
\\\\
x-3=\pm i\cdot3
\\\\
x-3=\pm 3i
\\\\
x=3\pm 3i
.\end{array}
Hence, $
x=\left\{ 3-3i,3+3i \right\}
.$
