Solve 2sqrt{x}=sqrt{x}

$$2 \sqrt { x } = \sqrt { x }$$

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{x}\right)^{2}=\left(\sqrt{x}\right)^{2}$$

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

$$4x=\left(\sqrt{x}\right)^{2}$$

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

$$4x=x$$

Subtract x from both sides.

$$4x-x=0$$

Combine 4x and -x to get 3x.

$$3x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 3 is not equal to 0, x must be equal to 0.

$$x=0$$

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

$$2\sqrt{0}=\sqrt{0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Equation 2\sqrt{x}=\sqrt{x} has a unique solution.

$$x=0$$