Answer
$z=4\pm3\sqrt{2}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
z^2-8z=2
,$ is
\begin{array}{l}\require{cancel}
z^2-8z+\left( \dfrac{-8}{2} \right)^2=2+\left( \dfrac{-8}{2} \right)^2
\\\\
z^2-8z+16=2+16
\\\\
(z-4)^2=18
\\\\
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}
