Answer
$x=1-i
\text{ OR }
x=1+i$
Work Step by Step
In the given equation,
\begin{align*}
x^2-2x+2=0
,\end{align*} $a=
1
,$ $b=
-2
,$ and $c=
2
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(2)}}{2(1)}
\\\\&=
\dfrac{2\pm\sqrt{4-8}}{2}
\\\\&=
\dfrac{2\pm\sqrt{-4}}{2}
\\\\&=
\dfrac{2\pm\sqrt{-1}\cdot\sqrt{4}}{2}
\\\\&=
\dfrac{2\pm\sqrt{-1}\cdot2}{2}
\\\\&=
\dfrac{2\pm i\cdot2}{2}
&\text{ (use $i=\sqrt{-1}$)}
\\\\&=
\dfrac{2\pm 2i}{2}
\\\\&=
\dfrac{\cancel2^1\pm \cancel2^1i}{\cancel2^1}
&\text{ (divide by $2$)}
\\\\&=
1\pm i
.\end{align*}
The solutions are $
x=1-i
\text{ and }
x=1+i
.$