#### Answer

$x=\left\{ 2-i\sqrt{7},2+ i\sqrt{7} \right\}$

#### 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-2)^2=-7
,$ are
\begin{array}{l}\require{cancel}
x-2=\pm\sqrt{-7}
\\\\
x-2=\pm\sqrt{-1}\cdot\sqrt{7}
\\\\
x-2=\pm i\sqrt{7}
\\\\
x=2\pm i\sqrt{7}
.\end{array}
Hence, $
x=\left\{ 2-i\sqrt{7},2+ i\sqrt{7} \right\}
.$