Solve y=-sqrt{4-x}

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

Solve for x

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

$$y\leq 0$$

Steps for Solving Radical Equations

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

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

Divide both sides by -1.

$$\frac{-\sqrt{-x+4}}{-1}=\frac{y}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{-x+4}=\frac{y}{-1}$$

Divide y by -1.

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

Square both sides of the equation.

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

Subtract 4 from both sides of the equation.

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

Subtracting 4 from itself leaves 0.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide y^{2}-4 by -1.

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

Solve for x (complex solution)

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

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

Solve for y

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

$$x\leq 4$$