Solve y=-3(sqrt{x-9}+12)

$$y = - 3 ( \sqrt { x - 9 } + 12 )$$

Solve for x

$$x=\frac{\left(y+36\right)^{2}+81}{9}$$

$$-\frac{y}{3}-12\geq 0$$

Steps for Solving Radical Equations

Use the distributive property to multiply -3 by \sqrt{x-9}+12.

$$y=-3\sqrt{x-9}-36$$

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

$$-3\sqrt{x-9}-36=y$$

Add 36 to both sides.

$$-3\sqrt{x-9}=y+36$$

Divide both sides by -3.

$$\frac{-3\sqrt{x-9}}{-3}=\frac{y+36}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$\sqrt{x-9}=\frac{y+36}{-3}$$

Divide 36+y by -3.

$$\sqrt{x-9}=-\frac{y}{3}-12$$

Square both sides of the equation.

$$x-9=\frac{\left(y+36\right)^{2}}{9}$$

Add 9 to both sides of the equation.

$$x-9-\left(-9\right)=\frac{\left(y+36\right)^{2}}{9}-\left(-9\right)$$

Subtracting -9 from itself leaves 0.

$$x=\frac{\left(y+36\right)^{2}}{9}-\left(-9\right)$$

Subtract -9 from \frac{\left(36+y\right)^{2}}{9}.

$$x=\frac{\left(y+36\right)^{2}}{9}+9$$

Solve for x (complex solution)

$$x=\frac{\left(y+36\right)^{2}+81}{9}$$

$$y=-36\text{ or }arg(\frac{y}{3}+12)\geq \pi$$

Solve for y (complex solution)

$$y=-3\sqrt{x-9}-36$$

Solve for y

$$y=-3\sqrt{x-9}-36$$

$$x\geq 9$$