Solve w=1/3sqrt{z-x}

$$w = \frac { 1 } { 3 } \sqrt { z - x }$$

Solve for x

$$x=z-9w^{2}$$

$$w\geq 0$$

Steps for Solving Radical Equations

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

$$\frac{1}{3}\sqrt{z-x}=w$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}\sqrt{-x+z}}{\frac{1}{3}}=\frac{w}{\frac{1}{3}}$$

Dividing by \frac{1}{3} undoes the multiplication by \frac{1}{3}.

$$\sqrt{-x+z}=\frac{w}{\frac{1}{3}}$$

Divide w by \frac{1}{3} by multiplying w by the reciprocal of \frac{1}{3}.

$$\sqrt{-x+z}=3w$$

Square both sides of the equation.

$$-x+z=9w^{2}$$

Subtract z from both sides of the equation.

$$-x+z-z=9w^{2}-z$$

Subtracting z from itself leaves 0.

$$-x=9w^{2}-z$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{9w^{2}-z}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{9w^{2}-z}{-1}$$

Divide 9w^{2}-z by -1.

$$x=z-9w^{2}$$

Solve for w

$$w=\frac{\sqrt{z-x}}{3}$$

$$z\geq x$$