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

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

Solve for x

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

Subtract 1 from both sides.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

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

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

Solve for y (complex solution)

$$y=\sqrt{2\left(x+1\right)}-1$$

$$y=-\sqrt{2\left(x+1\right)}-1$$

Solve for y

$$y=\sqrt{2\left(x+1\right)}-1$$

$$y=-\sqrt{2\left(x+1\right)}-1\text{, }x\geq -1$$