Solve y=-sqrt{x+2}-3

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

Solve for x

$$x=\left(y+3\right)^{2}-2$$

$$-\left(y+3\right)\geq 0$$

Steps for Solving Radical Equations

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

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

Add 3 to both sides.

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

Divide both sides by -1.

$$\frac{-\sqrt{x+2}}{-1}=\frac{y+3}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{x+2}=\frac{y+3}{-1}$$

Divide y+3 by -1.

$$\sqrt{x+2}=-\left(y+3\right)$$

Square both sides of the equation.

$$x+2=\left(y+3\right)^{2}$$

Subtract 2 from both sides of the equation.

$$x+2-2=\left(y+3\right)^{2}-2$$

Subtracting 2 from itself leaves 0.

$$x=\left(y+3\right)^{2}-2$$

Solve for x (complex solution)

$$x=\left(y+3\right)^{2}-2$$

$$y=-3\text{ or }arg(y+3)\geq \pi$$

Solve for y (complex solution)

$$y=-\left(\sqrt{x+2}+3\right)$$

Solve for y

$$y=-\left(\sqrt{x+2}+3\right)$$

$$x\geq -2$$