Solve y^2+4y+2x+1=0

$${ y }^{ 2 } +4y+2x+1=0$$

Solve for x

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

Steps for Solving Linear Equation

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

$$4y+2x+1=-y^{2}$$

Subtract 4y from both sides.

$$2x+1=-y^{2}-4y$$

Subtract 1 from both sides.

$$2x=-y^{2}-4y-1$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{-y^{2}-4y-1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{-y^{2}-4y-1}{2}$$

Divide -y^{2}-4y-1 by 2.

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

Solve for y (complex solution)

$$y=\sqrt{3-2x}-2$$

$$y=-\sqrt{3-2x}-2$$

Solve for y

$$y=\sqrt{3-2x}-2$$

$$y=-\sqrt{3-2x}-2\text{, }x\leq \frac{3}{2}$$