Answer
$\displaystyle \frac{1}{2}\pm\frac{1}{2}i$
Work Step by Step
$2x^{2}-2x+1=0$
We use the quadratic formula ($a=2, b=-2, c=1$):
$\displaystyle x=\frac{-(-2)\pm\sqrt{(-2)^{2}-4*2*1}}{2(2)}=\frac{2\pm\sqrt{4-8}}{4}=\frac{2\pm\sqrt{-4}}{4}=\frac{2\pm 2i}{4}=\frac{1}{2}\pm\frac{1}{2}i$