Answer
The solution set is $\color{blue}{\left\{1+\sqrt3, 1-\sqrt3\right\}}$.
Work Step by Step
Add $2$ to both sides:
$x^2-2x-2+2=0+2
\\x^2-2x=2$
Complete the square by adding $(\frac{-2}{2})^2=1$ to both sides:
$x^2-2x+1=2+1
\\x^2-2x+1=3$
Factor the trinomial:
$(x-1)^2= 3$
Take the square root of both sides:
$\sqrt{(x-1)^2}=\pm\sqrt{3}
\\x-1=\pm\sqrt{3}$
Add $1$ to both sides of the equation:
$x-1+1=1\pm\sqrt3
\\x=1\pm \sqrt3$
Thus, the solution set is $\color{blue}{\left\{1+\sqrt3, 1-\sqrt3\right\}}$.