What is the sum of all possible values of k for which x^2 + kx - 10x + 36 is the square of a binomial?
x^2 + (k - 10) + 36
square of a binomial = (x + b)^2 = x^2 + 2bx + b^2
The constant term is 36, so b is 6 or -6.
k - 10 = 12 or k - 10 = -12
k = 22 or k = -2