Solve y=-2sqrt{x+2}

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

Solve for x

$$x=\frac{y^{2}-8}{4}$$

$$y\leq 0$$

Steps for Solving Radical Equations

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

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

Divide both sides by -2.

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

Dividing by -2 undoes the multiplication by -2.

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

Divide y by -2.

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

Square both sides of the equation.

$$x+2=\frac{y^{2}}{4}$$

Subtract 2 from both sides of the equation.

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

Subtracting 2 from itself leaves 0.

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

Solve for x (complex solution)

$$x=\frac{y^{2}-8}{4}$$

$$arg(y)\geq \pi \text{ or }y=0$$

Solve for y

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

$$x\geq -2$$