Solve y=2sqrt{-x+3}

$$y = 2 \sqrt { - x + 3 }$$

Solve for x

$$x=-\frac{y^{2}}{4}+3$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$2\sqrt{-x+3}=y$$

Divide both sides by 2.

$$\frac{2\sqrt{-x+3}}{2}=\frac{y}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\sqrt{-x+3}=\frac{y}{2}$$

Square both sides of the equation.

$$-x+3=\frac{y^{2}}{4}$$

Subtract 3 from both sides of the equation.

$$-x+3-3=\frac{y^{2}}{4}-3$$

Subtracting 3 from itself leaves 0.

$$-x=\frac{y^{2}}{4}-3$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{\frac{y^{2}}{4}-3}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{\frac{y^{2}}{4}-3}{-1}$$

Divide \frac{y^{2}}{4}-3 by -1.

$$x=-\frac{y^{2}}{4}+3$$

Solve for x (complex solution)

$$x=-\frac{y^{2}}{4}+3$$

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

Solve for y (complex solution)

$$y=2\sqrt{3-x}$$

Solve for y

$$y=2\sqrt{3-x}$$

$$x\leq 3$$