Answer
$\left\{ -3-\sqrt{11},-3+\sqrt{11} \right\}$
Work Step by Step
The standard form of the given equation, $
x(x+6)=2
,$ is
\begin{array}{l}\require{cancel}
x^2+6x=2
\\\\
x^2+6x-2=0
.\end{array}
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the quadratic equation, $
x^2+6x-2=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(6)\pm\sqrt{(6)^2-4(1)(-2)}}{2(1)}
\\\\=
\dfrac{-6\pm\sqrt{36+8}}{2}
\\\\=
\dfrac{-6\pm\sqrt{44}}{2}
\\\\=
\dfrac{-6\pm\sqrt{4\cdot11}}{2}
\\\\=
\dfrac{-6\pm\sqrt{(2)^2\cdot11}}{2}
\\\\=
\dfrac{-6\pm2\sqrt{11}}{2}
\\\\=
\dfrac{2(-3\pm\sqrt{11})}{2}
\\\\=
\dfrac{\cancel{2}(-3\pm\sqrt{11})}{\cancel{2}}
\\\\=
-3\pm\sqrt{11}
.\end{array}
Hence, the solutions are $
\left\{ -3-\sqrt{11},-3+\sqrt{11} \right\}
.$
