Answer
$x=\dfrac{1}{2}\pm\dfrac{1}{2}i$
Work Step by Step
$2x^{2}-2x+1=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=2$, $b=-2$ and $c=1$.
Substitute the known values in the formula:
$x=\dfrac{-(-2)\pm\sqrt{(-2)^{2}-4(2)(1)}}{2(2)}=\dfrac{2\pm\sqrt{4-8}}{4}=...$
$...=\dfrac{2\pm\sqrt{-4}}{4}=\dfrac{2\pm2i}{4}=\dfrac{1}{2}\pm\dfrac{1}{2}i$
The answer is $x=\dfrac{1}{2}\pm\dfrac{1}{2}i$