Solve y=2sqrt{x}+2

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

Solve for x

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

$$-\left(-\frac{y}{2}+1\right)\geq 0$$

Steps for Solving Radical Equations

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

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

Subtract 2 from both sides.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide y-2 by 2.

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

Square both sides of the equation.

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

Solve for x (complex solution)

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

$$y=2\text{ or }arg(-\frac{y}{2}+1)\geq \pi$$

Solve for y (complex solution)

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

Solve for y

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

$$x\geq 0$$