Each solution to x^2 + 5x + 8 = 0 can be written in the form x = a + b i, where a$ and $b are real numbers. What is a + b^2?
Rewrite the expression g^4 + 12g^2 + 9 in the form c(g^2 + p)^2 + q. What is q?
x^2 + 5x + 8 = 0 complete the square on x
x^2 + 5x + 25/4 = -8 + 25/4
(x + 5/2)^2 = -32/4 + 25/4
(x + 5/2)^2 = -7/4 take both roots
(x + 5/2) = ± [ √7 / 2 ] i subtract 5/2 from both sides
x = -5/2 ± [√7 / 2 ] i
a =-5/2 b^2 = 7/4
So
a + b^2 = -5/2 + 7/4 = -10/4 + 7/4 = -3/4
Thank you!
g^4 + 12g^2 + 9 complete the square
g^4 + 12g^2 + 36 + 9 - 36 simplify
(g^2 + 6)^2 - 27
q = - 27