X^2+6x+90=0

A) x=-3+9i, - 3-9i

B) x=-12

C) x=6,-12

D) x=-3+9i

First, we con solve the quadratic by completing the squares

x^2 + 6x + 90 = 0

x^2 + 6x = - 90

x^2 + 6x + 9 = - 81 (to complete the square, half teh b calue squared gives us the c value)

(x + 3) ^2 = - 81

x + 3 = + √ (-81) and - √-81

x + 3 = 9i and - 9i

x = - 3 + 9i and - 3 - 9i

Choice A is correct