#### Answer

$x=\left\{ -8-\sqrt{11},-8+\sqrt{11} \right\}$

#### Work Step by Step

Taking the square root of both sides (the Square Root Property), the solutions to the given equation, $
(y+8)^2=11
,$ are
\begin{array}{l}\require{cancel}
y+8=\pm\sqrt{11}
\\\\
y=-8\pm\sqrt{11}
.\end{array}
Hence, $
x=\left\{ -8-\sqrt{11},-8+\sqrt{11} \right\}
.$