Solve y=3sqrt{x+6}

$$y=3 \sqrt{ x+6 }$$

Solve for x

$$x=\frac{y^{2}-54}{9}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$3\sqrt{x+6}=y$$

Divide both sides by 3.

$$\frac{3\sqrt{x+6}}{3}=\frac{y}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\sqrt{x+6}=\frac{y}{3}$$

Square both sides of the equation.

$$x+6=\frac{y^{2}}{9}$$

Subtract 6 from both sides of the equation.

$$x+6-6=\frac{y^{2}}{9}-6$$

Subtracting 6 from itself leaves 0.

$$x=\frac{y^{2}}{9}-6$$

Solve for x (complex solution)

$$x=\frac{y^{2}-54}{9}$$

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

Solve for y

$$y=3\sqrt{x+6}$$

$$x\geq -6$$