Solve y=2sqrt{x-4}-4

$$y = 2 \sqrt { x - 4 } - 4$$

Solve for x

$$x=\frac{\left(y+4\right)^{2}+16}{4}$$

$$\frac{y}{2}+2\geq 0$$

Steps for Solving Radical Equations

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

$$2\sqrt{x-4}-4=y$$

Add 4 to both sides.

$$2\sqrt{x-4}=y+4$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide y+4 by 2.

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

Square both sides of the equation.

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

Add 4 to both sides of the equation.

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

Subtracting -4 from itself leaves 0.

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

Subtract -4 from \frac{\left(y+4\right)^{2}}{4}.

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

Solve for x (complex solution)

$$x=\frac{\left(y+4\right)^{2}+16}{4}$$

$$y=-4\text{ or }arg(\frac{y}{2}+2)<\pi$$

Solve for y (complex solution)

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

Solve for y

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

$$x\geq 4$$