Solve 2y^2+16y-x+31=0

$$2 y ^ { 2 } + 16 y - x + 31 = 0$$

Solve for x

$$x=2y^{2}+16y+31$$

Steps for Solving Linear Equation

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

$$16y-x+31=-2y^{2}$$

Subtract 16y from both sides.

$$-x+31=-2y^{2}-16y$$

Subtract 31 from both sides.

$$-x=-2y^{2}-16y-31$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{-2y^{2}-16y-31}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{-2y^{2}-16y-31}{-1}$$

Divide -2y^{2}-16y-31 by -1.

$$x=2y^{2}+16y+31$$

Solve for y (complex solution)

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

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

Solve for y

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

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