Solve 46.75/x^2=13.9

$$\frac{ 46.75 }{ { x }^{ 2 } } = 13.9$$

Solve for x

$$x = \frac{\sqrt{259930}}{278} \approx 1.833932756$$

$$x = -\frac{\sqrt{259930}}{278} \approx -1.833932756$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$46.75=13.9x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$13.9x^{2}=46.75$$

Divide both sides by 13.9.

$$x^{2}=\frac{46.75}{13.9}$$

Expand \frac{46.75}{13.9} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{4675}{1390}$$

Reduce the fraction \frac{4675}{1390} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{935}{278}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{259930}}{278} x=-\frac{\sqrt{259930}}{278}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$46.75=13.9x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$13.9x^{2}=46.75$$

Subtract 46.75 from both sides.

$$13.9x^{2}-46.75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 13.9 for a, 0 for b, and -46.75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 13.9\left(-46.75\right)}}{2\times 13.9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 13.9\left(-46.75\right)}}{2\times 13.9}$$

Multiply -4 times 13.9.

$$x=\frac{0±\sqrt{-55.6\left(-46.75\right)}}{2\times 13.9}$$

Multiply -55.6 times -46.75 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{2599.3}}{2\times 13.9}$$

Take the square root of 2599.3.

$$x=\frac{0±\frac{\sqrt{259930}}{10}}{2\times 13.9}$$

Multiply 2 times 13.9.

$$x=\frac{0±\frac{\sqrt{259930}}{10}}{27.8}$$

Now solve the equation x=\frac{0±\frac{\sqrt{259930}}{10}}{27.8} when ± is plus.

$$x=\frac{\sqrt{259930}}{278}$$

Now solve the equation x=\frac{0±\frac{\sqrt{259930}}{10}}{27.8} when ± is minus.

$$x=-\frac{\sqrt{259930}}{278}$$

The equation is now solved.

$$x=\frac{\sqrt{259930}}{278} x=-\frac{\sqrt{259930}}{278}$$