Minima or what?

Algebra Level pending

The minimum value of \(2x^2+2xy+y^2+2x-3y+8\) for real numbers \(x\) and \(y\) is \(p\)\(.\) Then find the value of \(\lfloor p \rfloor\).

\[ \] Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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