Solve y=sqrt{2x+9}

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

Solve for x

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

$$y\geq 0$$

Steps for Solving Radical Equations

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

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

Square both sides of the equation.

$$2x+9=y^{2}$$

Subtract 9 from both sides of the equation.

$$2x+9-9=y^{2}-9$$

Subtracting 9 from itself leaves 0.

$$2x=y^{2}-9$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Solve for x (complex solution)

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

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

Solve for y

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

$$x\geq -\frac{9}{2}$$