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?

Guest Mar 15, 2021

#1**0 **

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)

=^._.^=

catmg Mar 15, 2021