Completing the Square

Geometry Level 5

$\large \begin{cases} xd+xc-yc+yd=0 & ...(1) \\ (d-y)(c-y)=(d+x)(c-x) & ... (2) \end{cases}$

For the above system of equations, $$c$$ and $$d$$ are positive constants, that $$x$$ and $$y$$ are non-zero, and that $$x+y$$ can be expressed in the form $$Ac^2+Bd^2+Cc+Dd+E$$, find the value of $$\lfloor A+B+C+D+E\rfloor$$.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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