Algebra

Having a double root means that the descriminant of the quadratic is 0. 

Let's simplify the equation. 

Combining all like terms and simplifying, we have

$x^2 + 15x + k$

Now, since the descriminant is 0, we have the equation

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

Thus, our final answer is 225/4. 

Thanks! :)