Solve y=sqrt{x-2}-2

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

Solve for x

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

$$y+2\geq 0$$

Steps for Solving Radical Equations

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

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

Add 2 to both sides.

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

Square both sides of the equation.

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

Add 2 to both sides of the equation.

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

Subtracting -2 from itself leaves 0.

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

Subtract -2 from \left(y+2\right)^{2}.

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

Solve for x (complex solution)

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

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

Solve for y

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

$$x\geq 2$$