Answer
$x=\left\{ 1-3i,1+ 3i \right\}$
Work Step by Step
Using the properties of equality, the given equation, $
x^2=2x-10
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2-2x+10=0
.\end{array}
The equation above has $a=1$, $b=-2$, and $c=10$.
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)(10)}}{2(1)}
\\\\
x=\dfrac{2\pm\sqrt{4-40}}{2}
\\\\
x=\dfrac{2\pm\sqrt{-36}}{2}
\\\\
x=\dfrac{2\pm\sqrt{-1}\cdot\sqrt{36}}{2}
\\\\
x=\dfrac{2\pm i\cdot\sqrt{(6)^2}}{2}
\\\\
x=\dfrac{2\pm 6i}{2}
\\\\
x=\dfrac{2(1\pm 3i)}{2}
\\\\
x=\dfrac{\cancel{2}(1\pm 3i)}{\cancel{2}}
\\\\
x=1\pm 3i
.\end{array}
Hence, the solutions are $
x=\left\{ 1-3i,1+ 3i \right\}
.$
