Solve y=-sqrt{9-x}

$$y = - \sqrt { 9 - x }$$

Solve for x

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

$$y\leq 0$$

Steps for Solving Radical Equations

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

$$-\sqrt{9-x}=y$$

Divide both sides by -1.

$$\frac{-\sqrt{-x+9}}{-1}=\frac{y}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{-x+9}=\frac{y}{-1}$$

Divide y by -1.

$$\sqrt{-x+9}=-y$$

Square both sides of the equation.

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

Subtract 9 from both sides of the equation.

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

Subtracting 9 from itself leaves 0.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

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

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

Solve for x (complex solution)

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

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

Solve for y

$$y=-\sqrt{9-x}$$

$$x\leq 9$$