Solve x=sqrt{(x/6})

$$x= \sqrt{ ( \frac{ x }{ 6 } } )$$

Solve for x

$$x=\frac{1}{6}\approx 0.166666667$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(\sqrt{\frac{x}{6}}\right)^{2}$$

Calculate \sqrt{\frac{x}{6}} to the power of 2 and get \frac{x}{6}.

$$x^{2}=\frac{x}{6}$$

Multiply both sides of the equation by 6.

$$6x^{2}=x$$

Subtract x from both sides.

$$6x^{2}-x=0$$

Factor out x.

$$x\left(6x-1\right)=0$$

To find equation solutions, solve x=0 and 6x-1=0.

$$x=0 x=\frac{1}{6}$$

Substitute 0 for x in the equation x=\sqrt{\frac{x}{6}}.

$$0=\sqrt{\frac{0}{6}}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{1}{6} for x in the equation x=\sqrt{\frac{x}{6}}.

$$\frac{1}{6}=\sqrt{\frac{\frac{1}{6}}{6}}$$

Simplify. The value x=\frac{1}{6} satisfies the equation.

$$\frac{1}{6}=\frac{1}{6}$$

List all solutions of x=\sqrt{\frac{x}{6}}.

$$x=0 x=\frac{1}{6}$$