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.

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

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