# 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.

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

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