Solve sqrt{z}x=pi-x

$$\sqrt{ z } x= \pi -x$$

Solve for x

$$x=\frac{\pi }{\sqrt{z}+1}$$

$$z\geq 0$$

Steps for Solving Linear Equation

Add x to both sides.

$$\sqrt{z}x+x=\pi$$

Combine all terms containing x.

$$\left(\sqrt{z}+1\right)x=\pi$$

Divide both sides by \sqrt{z}+1.

$$\frac{\left(\sqrt{z}+1\right)x}{\sqrt{z}+1}=\frac{\pi }{\sqrt{z}+1}$$

Dividing by \sqrt{z}+1 undoes the multiplication by \sqrt{z}+1.

$$x=\frac{\pi }{\sqrt{z}+1}$$

Solve for z

$$z=\left(-1+\frac{\pi }{x}\right)^{2}$$

$$x>0\text{ and }x\leq \pi$$

Steps for Solving Radical Equations

Divide both sides by x.

$$\frac{x\sqrt{z}}{x}=\frac{\pi -x}{x}$$

Dividing by x undoes the multiplication by x.

$$\sqrt{z}=\frac{\pi -x}{x}$$

Divide \pi -x by x.

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

Square both sides of the equation.

$$z=\frac{\left(\pi -x\right)^{2}}{x^{2}}$$