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 + b^2?
x^2 + 5x + 22 = 0
x = a + bi
(a+bi)^2 + 5(a+bi) + 22 = 0
a^2 - b^2 + 2abi + 5a + 5bi + 22 = 0
(a^2 - b^2 + 5a) + (2abi + 5bi) = -22
a^2 - b^2 + 5a = -22
2abi + 5bi = 0.
Can you solve it from here?
(Another method is to use the quadratic equation, as demestrated by ElectricPavlov here: https://web2.0calc.com/questions/help-me-plz-asap_1)