Solve x^2-y+2z^2=0

$$x ^ { 2 } - y + 2 z ^ { 2 } = 0$$

Solve for y

$$y=x^{2}+2z^{2}$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-y+2z^{2}=-x^{2}$$

Subtract 2z^{2} from both sides.

$$-y=-x^{2}-2z^{2}$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{-x^{2}-2z^{2}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{-x^{2}-2z^{2}}{-1}$$

Divide -x^{2}-2z^{2} by -1.

$$y=x^{2}+2z^{2}$$

Solve for x

$$x=\sqrt{y-2z^{2}}$$

$$x=-\sqrt{y-2z^{2}}\text{, }y\geq 2z^{2}$$