Solve sqrt{6x^2-x}=2x

$$\sqrt { 6 x ^ { 2 } - x } = 2 x$$

Solve for x

$$x=0$$

$$x=\frac{1}{2}=0.5$$

Solution Steps

Square both sides of the equation.

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

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

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

Expand \left(2x\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$6x^{2}-x=4x^{2}$$

Subtract 4x^{2} from both sides.

$$6x^{2}-x-4x^{2}=0$$

Combine 6x^{2} and -4x^{2} to get 2x^{2}.

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

Factor out x.

$$x\left(2x-1\right)=0$$

To find equation solutions, solve x=0 and 2x-1=0.

$$x=0 x=\frac{1}{2}$$

Substitute 0 for x in the equation \sqrt{6x^{2}-x}=2x.

$$\sqrt{6\times 0^{2}-0}=2\times 0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{1}{2} for x in the equation \sqrt{6x^{2}-x}=2x.

$$\sqrt{6\times \left(\frac{1}{2}\right)^{2}-\frac{1}{2}}=2\times \frac{1}{2}$$

Simplify. The value x=\frac{1}{2} satisfies the equation.

$$1=1$$

List all solutions of \sqrt{6x^{2}-x}=2x.

$$x=0 x=\frac{1}{2}$$