To find the solutions for the equations x^2 - 2x + 2 = 0 and x^2 - 3x + 2 = 0, we can use the quadratic formula:

For the equation x^2 - 2x + 2 = 0:
a = 1, b = -2, c = 2

Plugging these values into the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a)
x = (2 ± √((-2)^2 - 412))/(2*1)
x = (2 ± √(4 - 8))/2
x = (2 ± √(-4))/2
x = (2 ± 2i)/2
x = 1 ± i

Therefore, the solutions for x^2 - 2x + 2 = 0 are x = 1 + i and x = 1 - i.

For the equation x^2 - 3x + 2 = 0:
a = 1, b = -3, c = 2

Plugging these values into the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a)
x = (3 ± √((-3)^2 - 412))/(2*1)
x = (3 ± √(9 - 8))/2
x = (3 ± √1)/2
x = (3 ± 1)/2
x = 2 or x = 1

Therefore, the solutions for x^2 - 3x + 2 = 0 are x = 2 and x = 1.