Solve x-sqrt{y+1}=2

$$x- \sqrt{ y+1 } =2$$

Solve for y

$$y=\left(x-3\right)\left(x-1\right)$$

$$x-2\geq 0$$

Steps for Solving Radical Equations

Subtract x from both sides of the equation.

$$-\sqrt{y+1}+x-x=2-x$$

Subtracting x from itself leaves 0.

$$-\sqrt{y+1}=2-x$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide 2-x by -1.

$$\sqrt{y+1}=x-2$$

Square both sides of the equation.

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

Subtract 1 from both sides of the equation.

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

Subtracting 1 from itself leaves 0.

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

Subtract 1 from \left(x-2\right)^{2}.

$$y=\left(x-3\right)\left(x-1\right)$$

Solve for x (complex solution)

$$x=\sqrt{y+1}+2$$

Solve for y (complex solution)

$$y=\left(x-3\right)\left(x-1\right)$$

$$x=2\text{ or }arg(x-2)<\pi$$

Solve for x

$$x=\sqrt{y+1}+2$$

$$y\geq -1$$