Simplify $(\sqrt{x}) + x + 2 = (\sqrt{y}) + y + 2$ $\sqrt{x} + x + 2 = \sqrt{y} + y + 2$
I've simplified as follows:
$\sqrt{x} + x = \sqrt{y} + y$, square both sides
$x + x^2 = y + y^2$
It seems obvious that $x = y$ but I can’t get to that solution by algebraic means.

both $\sqrt{x}$ and $\sqrt{y}$ are roots of a quadratic equation:
$$
t^2+t + c=0
$$
hence either $\sqrt{x}=\sqrt{y}$ or $\sqrt{x}+\sqrt{y}=-1$
