Solve -x-sqrt{y+1}=2

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

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Add \sqrt{y+1} to both sides.

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

The equation is in standard form.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide 2+\sqrt{y+1} by -1.

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

Solve for x

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

$$y\geq -1$$

Steps for Solving Linear Equation

Add \sqrt{y+1} to both sides.

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

The equation is in standard form.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide 2+\sqrt{y+1} by -1.

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

Solve for y

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

$$x\leq -2$$

Steps for Solving Radical Equations

Subtract -x from both sides of the equation.

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

Subtracting -x from itself leaves 0.

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

Subtract -x from 2.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide 2+x by -1.

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

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(2+x\right)^{2}.

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

Solve for y (complex solution)

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

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