Solve frac{sqrt{x}}{x}=1/2

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

Solve for x

$$x=4$$

Solution Steps

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of x,2.

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

Subtract x from both sides.

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

Subtract -x from both sides of the equation.

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

Square both sides of the equation.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Subtract x^{2} from both sides.

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

Factor out x.

$$x\left(4-x\right)=0$$

To find equation solutions, solve x=0 and 4-x=0.

$$x=0 x=4$$

Substitute 0 for x in the equation \frac{\sqrt{x}}{x}=\frac{1}{2}. The expression is undefined.

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

Substitute 4 for x in the equation \frac{\sqrt{x}}{x}=\frac{1}{2}.

$$\frac{\sqrt{4}}{4}=\frac{1}{2}$$

Simplify. The value x=4 satisfies the equation.

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

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

$$x=4$$