Solve y=3sqrt{x+5}-2

$$y = 3 \sqrt { x + 5 } - 2$$

Solve for x

$$x=\frac{\left(y+2\right)^{2}-45}{9}$$

$$\frac{y+2}{3}\geq 0$$

Steps for Solving Radical Equations

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

$$3\sqrt{x+5}-2=y$$

Add 2 to both sides.

$$3\sqrt{x+5}=y+2$$

Divide both sides by 3.

$$\frac{3\sqrt{x+5}}{3}=\frac{y+2}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\sqrt{x+5}=\frac{y+2}{3}$$

Square both sides of the equation.

$$x+5=\frac{\left(y+2\right)^{2}}{9}$$

Subtract 5 from both sides of the equation.

$$x+5-5=\frac{\left(y+2\right)^{2}}{9}-5$$

Subtracting 5 from itself leaves 0.

$$x=\frac{\left(y+2\right)^{2}}{9}-5$$

Solve for x (complex solution)

$$x=\frac{\left(y+2\right)^{2}-45}{9}$$

$$y=-2\text{ or }arg(\frac{y+2}{3})<\pi$$

Solve for y

$$y=3\sqrt{x+5}-2$$

$$x\geq -5$$