HALP!!

x^2  - 2x  +  2  = 0    subtract 2 from both sides

x^2  - 2x  = - 2         complete the square on  x

x^2 - 2x + 1  = - 2  + 1        factor the left side and simplify

(x - 1)^2  =  - 1                   take both roots

x - 1  =  ±√(-1)

x -  1   = ± i          add 1 to both sides

x  =   1 ± i       

We could also use the quadratic formula for this problem. Substituting 1 in for a, -2 in for b, and 2 in for c, we get that the roots of x^2-2x+2 are (2 +- √4-8)/2, or 1 +- i, like CPhill got!