Find the roots of y=x^{2}+2x+2

y=x²+2x-3

Can solve using quadratic equation. Using the square method to obtain for the square term and x term (x+1)(x+1) = x²+2x+1

Therefore (x+1)(x+1)-4=y

To find roots equate to zero:     (x+1)(x+1)-4=0

Therefore:          (x+1)²=4

Which implies that:   x+1=+/-2

Therefore roots are x=-3 and x=1

Input these into the original equation to check and will see that these are correct.