#### Answer

$x=\left\{ -11,11 \right\}$

#### Work Step by Step

Taking the square root of both sides, the solutions to the given equation, $
x^2=121
,$ are
\begin{array}{l}\require{cancel}
x=\pm\sqrt{121}
\\\\
x=\pm\sqrt{(11)^2}
\\\\
x=\pm11
.\end{array}
Hence, the solution is $
x=\left\{ -11,11 \right\}
.$