Answer
$y=\left\{ -3-\sqrt{17},-3+\sqrt{17} \right\}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
y^2+6y-8=0
,$ is
\begin{array}{l}\require{cancel}
y^2+6y=8
\\\\
y^2+6y+\left( \dfrac{6}{2} \right)^2=8+\left( \dfrac{6}{2} \right)^2
\\\\
y^2+6y+9=8+9
\\\\
y^2+6y+9=17
\\\\
(y+3)^2=17
\\\\
y+3=\pm\sqrt{17}
\\\\
y=-3\pm\sqrt{17}
.\end{array}
Hence, $
y=\left\{ -3-\sqrt{17},-3+\sqrt{17} \right\}
.$
