Solve 8=sqrt{x^2-9y}

$$8 = \sqrt { x ^ { 2 } - 9 y }$$

Solve for y

$$y=\frac{x^{2}-64}{9}$$

Steps for Solving Radical Equations

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

$$\sqrt{x^{2}-9y}=8$$

Square both sides of the equation.

$$-9y+x^{2}=64$$

Subtract x^{2} from both sides of the equation.

$$-9y+x^{2}-x^{2}=64-x^{2}$$

Subtracting x^{2} from itself leaves 0.

$$-9y=64-x^{2}$$

Divide both sides by -9.

$$\frac{-9y}{-9}=\frac{64-x^{2}}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$y=\frac{64-x^{2}}{-9}$$

Divide -x^{2}+64 by -9.

$$y=\frac{x^{2}-64}{9}$$

Solve for x (complex solution)

$$x=-\sqrt{9y+64}$$

$$x=\sqrt{9y+64}$$

Solve for x

$$x=\sqrt{9y+64}$$

$$x=-\sqrt{9y+64}\text{, }y\geq -\frac{64}{9}$$