Answer
$x=\left\{ 1- 2i,1+ 2i \right\}$
Work Step by Step
Using the properties of equality, the given equation, $
x^2=2x-5
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2-2x+5=0
.\end{array}
The equation above has $a=1$, $b=-2$, and $c=5$.
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions to the equation above are
\begin{array}{l}\require{cancel}
x=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(5)}}{2(1)}
\\\\
x=\dfrac{2\pm\sqrt{4-20}}{2}
\\\\
x=\dfrac{2\pm\sqrt{-16}}{2}
\\\\
x=\dfrac{2\pm\sqrt{-1}\cdot\sqrt{16}}{2}
\\\\
x=\dfrac{2\pm i\sqrt{(4)^2}}{2}
\\\\
x=\dfrac{2\pm 4i}{2}
\\\\
x=\dfrac{2(1\pm 2i)}{2}
\\\\
x=\dfrac{\cancel{2}(1\pm 2i)}{\cancel{2}}
\\\\
x=1\pm 2i
.\end{array}
Hence, the solutions are $
x=\left\{ 1- 2i,1+ 2i \right\}
.$