Solve sqrt{z}x=pi*x

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

Solve for x

$$\left\{\begin{matrix}x=0\text{, }&z\geq 0\\x\in \mathrm{R}\text{, }&z=\pi ^{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \pi x from both sides.

$$\sqrt{z}x-\pi x=0$$

Combine all terms containing x.

$$\left(\sqrt{z}-\pi \right)x=0$$

Divide 0 by \sqrt{z}-\pi .

$$x=0$$

Solve for z

$$\left\{\begin{matrix}\\z=\pi ^{2}\text{, }&\text{unconditionally}\\z\geq 0\text{, }&x=0\end{matrix}\right.$$

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.

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

Square both sides of the equation.

$$z=\pi ^{2}$$