Solving a quadratic using a system of equations

Algebra Level 3

If $\begin{cases} a + b = 40 \\ b + c = 3 \\ a + c = -11 \end{cases}$ where $a$ , $b$ and $c$ are real numbers, and that $a + b + c = k$ , then find $x$ that satisfies the following equation.

$\frac{kx^2}{4} - 44kx + 1933k = -48$