Solve y=sqrt{6-2x}

$$y = \sqrt { 6 - 2 x }$$

Solve for x

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

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{6-2x}=y$$

Square both sides of the equation.

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

Subtract 6 from both sides of the equation.

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

Subtracting 6 from itself leaves 0.

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

Divide both sides by -2.

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

Dividing by -2 undoes the multiplication by -2.

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

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

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

Solve for x (complex solution)

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

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

Solve for y

$$y=\sqrt{6-2x}$$

$$x\leq 3$$