Answer
The solutions are $x=1\pm3i$
Work Step by Step
$x^{2}=2x-10$
Take all terms to the left side of the equation:
$x^{2}-2x+10=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. In this case, $a=1$, $b=-2$ and $c=10$
Substitute the known values into the formula and evaluate:
$x=\dfrac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(10)}}{2(1)}=\dfrac{2\pm\sqrt{4-40}}{2}=...$
$...=\dfrac{2\pm\sqrt{-36}}{2}=\dfrac{2\pm6i}{2}=\dfrac{2}{2}\pm\dfrac{6}{2}i=1\pm3i$
The solutions are $x=1\pm3i$
