#### Answer

$x=\left\{ 1-i\sqrt{13},1+ i\sqrt{13} \right\}$

#### 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-1)^2=-13
,$ are
\begin{array}{l}\require{cancel}
x-1=\pm\sqrt{-13}
\\\\
x-1=\pm\sqrt{-1}\cdot\sqrt{13}
\\\\
x-1=\pm i\sqrt{13}
\\\\
x=1\pm i\sqrt{13}
.\end{array}
Hence, $
x=\left\{ 1-i\sqrt{13},1+ i\sqrt{13} \right\}
.$