Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.
x^2 + (k - 9)x + 16
We need to have the discriminant = 0
(k - 9)^2 - 4 * 16 = 0
(k -9)^2 - 64 = 0
(k -9)^2 = 64 take both roots
k - 9 = 8 k -9 = -8
k =17 k = 1
Sum of k's = 17 + 1 = 18
+1859 
