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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?

 Mar 15, 2021
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 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) 

 

=^._.^=

 Mar 15, 2021

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