Algebra

First, let's combine all like terms and simplify. We have

$x^2 + 15x + k$ as the simplified version. 

To have a double root means that the descriminant is 0. 

The descriminant is in the form of $b^2-4ac$, so we have the equation

$15^2 - 4 (1)(k) = 0 \\ 225 - 4k = 0\\ 225 = 4k \\ k = 225 / 4$

Thus, our answer is 225/4. 

Thanks! :)