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.

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