[tex]\displaystyle\sf\\x^2-2x-2=0 \Leftrightarrow x^2-2x=2 |+1 \implies x^2-2x+1=3 \Leftrightarrow\\(x-1)^2=3 \implies x-1=\pm\sqrt{3} \implies x\in\left\{\sqrt{3}+1, 1-\sqrt{3}\right\}.[/tex]