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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