Solve y=2sqrt{x-2}

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

Solve for x

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

$$y\geq 0$$

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.

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

Square both sides of the equation.

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

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=\frac{y^{2}}{4}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=\frac{y^{2}}{4}-\left(-2\right)$$

Subtract -2 from \frac{y^{2}}{4}.

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

Solve for x (complex solution)

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

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

Solve for y

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

$$x\geq 2$$