Answer
The solutions are $x=3\pm2i$
Work Step by Step
$x^{2}-6x+13=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.
In this case, $a=1$, $b=-6$ and $c=13$
Substitute the known values into the formula and evaluate:
$x=\dfrac{-(-6)\pm\sqrt{(-6)^{2}-4(1)(13)}}{2(1)}=\dfrac{6\pm\sqrt{36-52}}{2}=...$
$...=\dfrac{6\pm\sqrt{-16}}{2}=\dfrac{6\pm4i}{2}=3\pm2i$
