Question

$$2x^{2}+2y^{2}-8x+5y+10=0$$

Solve for x (complex solution)

$x=\frac{\sqrt{-4y^{2}-10y-4}}{2}+2$
$x=-\frac{\sqrt{-4y^{2}-10y-4}}{2}+2$

Solve for y (complex solution)

$y=\frac{\sqrt{-16x^{2}+64x-55}-5}{4}$
$y=\frac{-\sqrt{-16x^{2}+64x-55}-5}{4}$

Solve for x

$x=\frac{\sqrt{-4y^{2}-10y-4}}{2}+2$
$x=-\frac{\sqrt{-4y^{2}-10y-4}}{2}+2\text{, }y\geq -2\text{ and }y\leq -\frac{1}{2}$

Solve for y

$y=\frac{\sqrt{-16x^{2}+64x-55}-5}{4}$
$y=\frac{-\sqrt{-16x^{2}+64x-55}-5}{4}\text{, }x\geq \frac{5}{4}\text{ and }x\leq \frac{11}{4}$