Chapter 8 - Section 8.5 - Quadratic Functions and Their Graphs - Exercise Set - Page 519: 63

$z=-5\pm\sqrt{26}$

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}