Given that x = -5 is a root to the quadratic 2x^2 + px - 15 = 0, and the quadratic equation p(x^2 + x) + k = 0 has equal roots, find k.
Plug in \(x = -5\) into the first equation. Because it is a root, this equation will be true.
Solving for p gives us: \(p = 7\).
Now, plugging this in the second equation gives us: \(7x^2 + 7x + k = 0 \)
For the equation to have 1 solution, the discriminant must equal 0.
Can you take it from here?