Solve 7/5xsqrt{frac{7521{396}}}=e

$$\frac{ 7 }{ 5x \sqrt{ \frac{ 7521 }{ 396 } } } =e$$

Solve for x

$$x=\frac{14\sqrt{82731}}{12535e}\approx 0.118179828$$

Steps for Solving Linear Equation

Reduce the fraction \frac{7521}{396} to lowest terms by extracting and canceling out 3.

$$\frac{7}{5x\sqrt{\frac{2507}{132}}}=e$$

Rewrite the square root of the division \sqrt{\frac{2507}{132}} as the division of square roots \frac{\sqrt{2507}}{\sqrt{132}}.

$$\frac{7}{5x\times \frac{\sqrt{2507}}{\sqrt{132}}}=e$$

Factor 132=2^{2}\times 33. Rewrite the square root of the product \sqrt{2^{2}\times 33} as the product of square roots \sqrt{2^{2}}\sqrt{33}. Take the square root of 2^{2}.

$$\frac{7}{5x\times \frac{\sqrt{2507}}{2\sqrt{33}}}=e$$

Rationalize the denominator of \frac{\sqrt{2507}}{2\sqrt{33}} by multiplying numerator and denominator by \sqrt{33}.

$$\frac{7}{5x\times \frac{\sqrt{2507}\sqrt{33}}{2\left(\sqrt{33}\right)^{2}}}=e$$

The square of \sqrt{33} is 33.

$$\frac{7}{5x\times \frac{\sqrt{2507}\sqrt{33}}{2\times 33}}=e$$

To multiply \sqrt{2507} and \sqrt{33}, multiply the numbers under the square root.

$$\frac{7}{5x\times \frac{\sqrt{82731}}{2\times 33}}=e$$

Multiply 2 and 33 to get 66.

$$\frac{7}{5x\times \frac{\sqrt{82731}}{66}}=e$$

Express 5\times \frac{\sqrt{82731}}{66} as a single fraction.

$$\frac{7}{\frac{5\sqrt{82731}}{66}x}=e$$

Express \frac{5\sqrt{82731}}{66}x as a single fraction.

$$\frac{7}{\frac{5\sqrt{82731}x}{66}}=e$$

Divide 7 by \frac{5\sqrt{82731}x}{66} by multiplying 7 by the reciprocal of \frac{5\sqrt{82731}x}{66}.

$$\frac{7\times 66}{5\sqrt{82731}x}=e$$

Rationalize the denominator of \frac{7\times 66}{5\sqrt{82731}x} by multiplying numerator and denominator by \sqrt{82731}.

$$\frac{7\times 66\sqrt{82731}}{5\left(\sqrt{82731}\right)^{2}x}=e$$

The square of \sqrt{82731} is 82731.

$$\frac{7\times 66\sqrt{82731}}{5\times 82731x}=e$$

Multiply 7 and 66 to get 462.

$$\frac{462\sqrt{82731}}{5\times 82731x}=e$$

Multiply 5 and 82731 to get 413655.

$$\frac{462\sqrt{82731}}{413655x}=e$$

Cancel out 33 in both numerator and denominator.

$$\frac{14\sqrt{82731}}{12535x}=e$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12535x.

$$14\sqrt{82731}=e\times 12535x$$

Reorder the terms.

$$14\sqrt{82731}=12535ex$$

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

$$12535ex=14\sqrt{82731}$$

Divide both sides by 12535e.

$$\frac{12535ex}{12535e}=\frac{14\sqrt{82731}}{12535e}$$

Dividing by 12535e undoes the multiplication by 12535e.

$$x=\frac{14\sqrt{82731}}{12535e}$$

Variable x cannot be equal to 0.

$$x=\frac{14\sqrt{82731}}{12535e}\text{, }x\neq 0$$