Answer
$x=1\pm\sqrt{3}$
Work Step by Step
Using the completing the square method, then,
\begin{array}{l}
x^2-2x-2=0\\
x^2-2x=2\\
x^2-2x+\left( \dfrac{-2}{2} \right)^2=2+\left( \dfrac{-2}{2}\right)^2\\
x^2-2x+1=2+1\\
(x-1)^2=3\\
x-1=\pm\sqrt{3}\\
x=1\pm\sqrt{3}
.\end{array}