Solve r=sqrt{10r}

$$r = \sqrt { 10 r }$$

Solve for r

$$r=10$$

$$r=0$$

Solution Steps

Square both sides of the equation.

$$r^{2}=\left(\sqrt{10r}\right)^{2}$$

Calculate \sqrt{10r} to the power of 2 and get 10r.

$$r^{2}=10r$$

Subtract 10r from both sides.

$$r^{2}-10r=0$$

Factor out r.

$$r\left(r-10\right)=0$$

To find equation solutions, solve r=0 and r-10=0.

$$r=0 r=10$$

Substitute 0 for r in the equation r=\sqrt{10r}.

$$0=\sqrt{10\times 0}$$

Simplify. The value r=0 satisfies the equation.

$$0=0$$

Substitute 10 for r in the equation r=\sqrt{10r}.

$$10=\sqrt{10\times 10}$$

Simplify. The value r=10 satisfies the equation.

$$10=10$$

List all solutions of r=\sqrt{10r}.

$$r=0 r=10$$