Solve y=sqrt{-x+3}

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

Solve for x

$$x=3-y^{2}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

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

Square both sides of the equation.

$$-x+3=y^{2}$$

Subtract 3 from both sides of the equation.

$$-x+3-3=y^{2}-3$$

Subtracting 3 from itself leaves 0.

$$-x=y^{2}-3$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide y^{2}-3 by -1.

$$x=3-y^{2}$$

Solve for x (complex solution)

$$x=3-y^{2}$$

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

Solve for y (complex solution)

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

Solve for y

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

$$x\leq 3$$