Solve y+2=sqrt{9+x}

$$y + 2 = \sqrt { 9 + x }$$

Solve for x

$$x=\left(y-1\right)\left(y+5\right)$$

$$y+2\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{9+x}=y+2$$

Square both sides of the equation.

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

Subtract 9 from both sides of the equation.

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

Subtracting 9 from itself leaves 0.

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

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

$$x=\left(y-1\right)\left(y+5\right)$$

Solve for x (complex solution)

$$x=\left(y-1\right)\left(y+5\right)$$

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

Solve for y (complex solution)

$$y=\sqrt{x+9}-2$$

Solve for y

$$y=\sqrt{x+9}-2$$

$$x\geq -9$$