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Math·Advanced Math·Nonlinear equations in one variable and systems of equations in two variables

hard

$$\begin{array}{rl}y& =x-c\\ y& =-6(x-12{)}^2\end{array}$$

In the given system of equations, $c$ is a constant. The system has two distinct real solutions. Which of the following could be the value of $c$?

A

$7$

B

$11$

C

$\frac{287}{24}$

D

$17$