using the quadratic formula to find the roots (solutions) of any equation of the form: ax² + bx + c = 0

x = (-b±√(b² - 4ac))/2a

applied to our equation x² - 2x + 1 = 2 after we make the right side equals 0 it becomes x² - 2x - 1 = 0

so from it we can read that   a=1, b=-2, c=-1

pluging these values for a,b and c in the quadratic formula above to find the x values we have

x =( -(-2)±√( (-2)² -4(1)(-1) ) )/2*1 = ( 2 ± √8 )/2 = ( 2 ± √(2*4) )/2 = ( 2 ± √4 * √2)/2 = ( 2 ± 2√2)/2 = 2/2 ± 2√2/2 = 1 ± √2

So x values are x= 1 + √2 and x= 1 - √2