+2653 Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.
+1926 Combining all like terms in the equation,
\(x^2 + (k-9)x + 16\)
In order for this to be the square of a binomial, the coefficient of x has to be 2 times the square root of the third term.
Take this
\((x+b)^2=x^2+2bx+b^2\)
2b is exactly two times the square root of the third term.
In this case, we have \(k-9=2\sqrt{16}\)
We have
\(k-9=8\\ k=17\)
So k is 17.
Thanks! :)
