+313 Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.
+37159 This just means that the discriminant is = 0 ( double root)
x^2 + (k-9) x +16 = 0
b^2 - 4ac = 0
(k-9)^2 - 4(1)(16)
k^2 - 18k + 81 - 64 = 0
k^2 - 18k + 17 = 0 Use quadratic formula to find k = 1 or 17
Another way:
if (1/2(k-9)) ^2 = 16 this will be ( via 'completing the square' for 'x' )
1/2k - 4.5 = +- 4
1/2 k = .5 or 8.5
k = 1 or 17
