What is the sum of all possible values of for which x^2 + kx - 10x + 36 -32 is the square of a binomial?
We can simplify this equation to: \(x^2 + kx- 10x + 4\).
Factoring out x gives us: \(x^2 + x(k-10) +4\)
For the quadratic to have only 1 solution, the discriminant(\(b^2 - 4ac\)) must be equal to 0.
Substituting what we know, we have: \((k-10)^2 - 16 = 0\)
Adding 16 to both sides gives us: \((k-10)^2 = 16\)
Taking the square root of both sides gives us: \(k - 10 = \pm 4\).
Now, we can find the 2 values of \(k\) and add them up.
Can you take it from here?