Solve y=-sqrt{-x+6/1}

$$y = - \sqrt { \frac { - x + 6 } { 1 } }$$

Solve for x

$$x=6-y^{2}$$

$$y\leq 0$$

Steps for Solving Radical Equations

Anything divided by one gives itself.

$$y=-\sqrt{-x+6}$$

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

$$-\sqrt{-x+6}=y$$

Divide both sides by -1.

$$\frac{-\sqrt{-x+6}}{-1}=\frac{y}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{-x+6}=\frac{y}{-1}$$

Divide y by -1.

$$\sqrt{-x+6}=-y$$

Square both sides of the equation.

$$-x+6=y^{2}$$

Subtract 6 from both sides of the equation.

$$-x+6-6=y^{2}-6$$

Subtracting 6 from itself leaves 0.

$$-x=y^{2}-6$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{y^{2}-6}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{y^{2}-6}{-1}$$

Divide y^{2}-6 by -1.

$$x=6-y^{2}$$

Solve for x (complex solution)

$$x=6-y^{2}$$

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

Solve for y (complex solution)

$$y=-\sqrt{6-x}$$

Solve for y

$$y=-\sqrt{6-x}$$

$$x\leq 6$$