Solve frac{sqrt{x}}{x}=3.14

$$\frac { \sqrt { x } } { x } = 3.14$$

Solve for x

$$x=\frac{2500}{24649}\approx 0.101423993$$

Solution Steps

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

$$\sqrt{x}=3.14x$$

Square both sides of the equation.

$$\left(\sqrt{x}\right)^{2}=\left(3.14x\right)^{2}$$

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

$$x=\left(3.14x\right)^{2}$$

Expand \left(3.14x\right)^{2}.

$$x=3.14^{2}x^{2}$$

Calculate 3.14 to the power of 2 and get 9.8596.

$$x=9.8596x^{2}$$

Subtract 9.8596x^{2} from both sides.

$$x-9.8596x^{2}=0$$

Factor out x.

$$x\left(1-9.8596x\right)=0$$

To find equation solutions, solve x=0 and 1-\frac{24649x}{2500}=0.

$$x=0 x=\frac{2500}{24649}$$

Substitute 0 for x in the equation \frac{\sqrt{x}}{x}=3.14. The expression is undefined.

$$\frac{\sqrt{0}}{0}=3.14$$

Substitute \frac{2500}{24649} for x in the equation \frac{\sqrt{x}}{x}=3.14.

$$\frac{\sqrt{\frac{2500}{24649}}}{\frac{2500}{24649}}=3.14$$

Simplify. The value x=\frac{2500}{24649} satisfies the equation.

$$\frac{157}{50}=3.14$$

Equation \sqrt{x}=\frac{157x}{50} has a unique solution.

$$x=\frac{2500}{24649}$$