#### Answer

$x=\left\{ 4-3\sqrt{2},4+3\sqrt{2} \right\}$

#### Work Step by Step

Taking the square root of both sides (the Square Root Property), the solutions to the given equation, $
(z-4)^2=18
,$ are
\begin{array}{l}\require{cancel}
z-4=\pm\sqrt{18}
\\\\
z-4=\pm\sqrt{9\cdot2}
\\\\
z-4=\pm\sqrt{(3)^2\cdot2}
\\\\
z-4=\pm3\sqrt{2}
\\\\
z=4\pm3\sqrt{2}
.\end{array}
Hence, $
x=\left\{ 4-3\sqrt{2},4+3\sqrt{2} \right\}
.$