Solve y=-3sqrt{2-x}

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

Solve for x

$$x=-\frac{y^{2}}{9}+2$$

$$y\leq 0$$

Steps for Solving Radical Equations

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

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

Divide both sides by -3.

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

Dividing by -3 undoes the multiplication by -3.

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

Divide y by -3.

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

Square both sides of the equation.

$$-x+2=\frac{y^{2}}{9}$$

Subtract 2 from both sides of the equation.

$$-x+2-2=\frac{y^{2}}{9}-2$$

Subtracting 2 from itself leaves 0.

$$-x=\frac{y^{2}}{9}-2$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{\frac{y^{2}}{9}-2}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{\frac{y^{2}}{9}-2}{-1}$$

Divide \frac{y^{2}}{9}-2 by -1.

$$x=-\frac{y^{2}}{9}+2$$

Solve for x (complex solution)

$$x=-\frac{y^{2}}{9}+2$$

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

Solve for y

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

$$x\leq 2$$