Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.
Simplify as
x^2 + (k - 9)x + 16
Note that
(x + 4) (x + 4) = x^2 + 8x + 16 = (x + 4)^2
So
k -9 = 8
k =17
Also
(x - 4) (x -4) = x^2 - 8x + 16 = (x - 4)^2
k- 9 = -8
k = 1
17 + 1 = 18
+1725 
