+501 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 $a + b^2$?
+128460 x^2 + 5x + 8 = 0 complete the square on x
x^2 + 5x = -8 take 1/2 of 5 = 5/2....square it = 25/4.....add to both sides of the equation
x^2 + 5x + 25/4 = -8 + 25/4 factor the left....simplify the right
(x + 5/2) ^2 = -32/4 + 25/4
( x + 5/2)^2 = - 7/4 we only need one root
x + 5/2 = √7i / 2
x = -5/2 + (√7/2) i
a + b^2 = -5/2 + (√7/2)^2 = -5/2 + 7/4 = -10/4 + 7/4 = -3/4
