Answer
$y=\left\{ -3-3i\sqrt{2},-3+3i\sqrt{2} \right\}$
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, $
(y+3)^2=-18
,$ are
\begin{array}{l}\require{cancel}
y+3=\pm\sqrt{-18}
\\\\
y+3=\pm\sqrt{-1}\cdot\sqrt{18}
\\\\
y+3=\pm i\cdot\sqrt{9\cdot2}
\\\\
y+3=\pm i\cdot\sqrt{(3)^2\cdot2}
\\\\
y+3=\pm i\cdot3\sqrt{2}
\\\\
y+3=\pm 3i\sqrt{2}
\\\\
y=-3\pm 3i\sqrt{2}
.\end{array}
Hence, $
y=\left\{ -3-3i\sqrt{2},-3+3i\sqrt{2} \right\}
.$
