Solve y=2sqrt{4-x}

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

Solve for x

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

$$y\geq 0$$

Steps for Solving Radical Equations

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

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Square both sides of the equation.

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

Subtract 4 from both sides of the equation.

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

Subtracting 4 from itself leaves 0.

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

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{\frac{y^{2}}{4}-4}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{\frac{y^{2}}{4}-4}{-1}$$

Divide -4+\frac{y^{2}}{4} by -1.

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

Solve for x (complex solution)

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

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

Solve for y

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

$$x\leq 4$$