Answer
$x=\dfrac{3}{2}\pm\dfrac{\sqrt{3}}{2}i$
Work Step by Step
$x^{2}-3x+3=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=1$, $b=-3$ and $c=3$.
Substitute the known values in the formula:
$x=\dfrac{-(-3)\pm\sqrt{(-3)^{2}-4(1)(3)}}{2(1)}=\dfrac{3\pm\sqrt{9-12}}{2}=...$
$...=\dfrac{3\pm\sqrt{-3}}{2}=\dfrac{3\pm\sqrt{3}i}{2}=\dfrac{3}{2}\pm\dfrac{\sqrt{3}}{2}i$
The answer is $x=\dfrac{3}{2}\pm\dfrac{\sqrt{3}}{2}i$
