\(A=\left(-2x^2+4xy-2y^2\right)-8\left(x-y\right)-8-2y^2-20y-50+63\\ A=\left[-2\left(x-y\right)^2-8\left(x-y\right)-8\right]-2\left(y^2+10y+25\right)+63\\ A=-2\left(x-y+2\right)^2-2\left(y+5\right)^2+63\le63\\ A_{max}=63\Leftrightarrow\left\{{}\begin{matrix}x=y-2=-7\\y=-5\end{matrix}\right.\)
\(A=\left(-2x^2+4xy-2y^2\right)-8\left(x-y\right)-8-2y^2-20y-50+63\\ A=\left[-2\left(x-y\right)^2-8\left(x-y\right)-8\right]-2\left(y^2+10y+25\right)+63\\ A=-2\left(x-y+2\right)^2-2\left(y+10\right)^2+63\le63\\ A_{max}=63\Leftrightarrow\left\{{}\begin{matrix}x=y-2=-12\\y=-10\end{matrix}\right.\)
