Solve x^2+4y+2z=25+2y

$${ x }^{ 2 } +4y+2z = 25+2y$$

Solve for y

$$y=-\frac{x^{2}}{2}-z+\frac{25}{2}$$

Steps for Solving Linear Equation

Subtract 2y from both sides.

$$x^{2}+4y+2z-2y=25$$

Combine 4y and -2y to get 2y.

$$x^{2}+2y+2z=25$$

Subtract x^{2} from both sides.

$$2y+2z=25-x^{2}$$

Subtract 2z from both sides.

$$2y=25-x^{2}-2z$$

The equation is in standard form.

$$2y=25-2z-x^{2}$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{25-2z-x^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{25-2z-x^{2}}{2}$$

Divide 25-x^{2}-2z by 2.

$$y=-\frac{x^{2}}{2}-z+\frac{25}{2}$$

Solve for x (complex solution)

$$x=-\sqrt{25-2z-2y}$$

$$x=\sqrt{25-2z-2y}$$

Solve for x

$$x=\sqrt{25-2z-2y}$$

$$x=-\sqrt{25-2z-2y}\text{, }y\leq \frac{25}{2}-z$$