Solve for y
y=-\frac{z^{2}-x^{2}}{2}
Solve for x
x=\sqrt{2y+z^{2}}
x=-\sqrt{2y+z^{2}}\text{, }y\geq -\frac{z^{2}}{2}
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z^{2}+2y=x^{2}
Swap sides so that all variable terms are on the left hand side.
2y=x^{2}-z^{2}
Subtract z^{2} from both sides.
\frac{2y}{2}=\frac{\left(x-z\right)\left(x+z\right)}{2}
Divide both sides by 2.
y=\frac{\left(x-z\right)\left(x+z\right)}{2}
Dividing by 2 undoes the multiplication by 2.
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