There are two values of $a$ for which the equation $4x^2+ax+8x+9=0$ has only one solution for $x$. What is the sum of those values of $a$?
4x^2 + ax + 8x + 9 = 0
4x^2 + (8 + a)x + 9 = 0
If one solution, the discriminant = 0....so....
(8 + a)^2 - 4(4)(9) = 0
64 + 16a + a^2 - 144 = 0 simplify
a^2 + 16a - 80 = 0 factor
(a + 20) ( a - 4) = 0
Setting both factors to 0 and solving for a gives that a = -20 or a = 4
And the sum of these = -16