+779 Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.
+1804 Let's first combine all like terms. We have
\(x^2+kx-9x+16\\ x^2+(k-9)x+16\)
Since we need this to be a difference of squares, k-9 must be 2 times the square root of 16.
Thus, we have
\(k-9=8\\ k=17\)
So k is 17.
So our answer is 17.
Thanks! :)
