Algebra

First, let's combine all like terms and reaarange so we have the shape of a quadratic formula. 

We get

$x^2 + 15x + k$

Having a double root means that the descriminant is greater than 0, so we have the equation

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

thus, The value of k is $k = 225 / 4$

Thanks! :)