Each solution to x^2 + 5x + 8 = -14 can be written in the form a + bi where a and b are real numbers. What is a^2 + b^2?
This problem avoids direct vieta's formulas! Smart!
We know that a^2 + b^2 = (a + bi)(a - bi), which are just the product of the roots!
x^2 + 5x + 22 = 0
By vieta's, the product of the roots is -22.