Answer
$x=\left\{ -12-10i,-12+10i \right\}$
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+12)^2=-100
,$ are
\begin{array}{l}\require{cancel}
x+12=\pm\sqrt{-100}
\\\\
x+12=\pm\sqrt{-1}\cdot\sqrt{100}
\\\\
x+12=\pm i\cdot\sqrt{(10)^2}
\\\\
x+12=\pm i\cdot10
\\\\
x+12=\pm 10i
\\\\
x=-12\pm 10i
.\end{array}
Hence, $
x=\left\{ -12-10i,-12+10i \right\}
.$
