Answer
$z=-5\pm\sqrt{26}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
z^2+10z-1=0
,$ is
\begin{array}{l}\require{cancel}
z^2+10z=1
\\\\
z^2+10z+\left( \dfrac{10}{2} \right)^2=1+\left( \dfrac{10}{2} \right)^2
\\\\
z^2+10z+25=1+25
\\\\
(z+5)^2=26
\\\\
z+5=\pm\sqrt{26}
\\\\
z=-5\pm\sqrt{26}
.\end{array}