Solve 13/x*7/x=7

$$\frac{ 13 }{ x } \times \frac{ 7 }{ x } =7$$

Solve for x

$$x=\sqrt{13}\approx 3.605551275$$

$$x=-\sqrt{13}\approx -3.605551275$$

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.

$$13\times \frac{7}{x}=7x$$

Express 13\times \frac{7}{x} as a single fraction.

$$\frac{13\times 7}{x}=7x$$

Multiply 13 and 7 to get 91.

$$\frac{91}{x}=7x$$

Subtract 7x from both sides.

$$\frac{91}{x}-7x=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -7x times \frac{x}{x}.

$$\frac{91}{x}+\frac{-7xx}{x}=0$$

Since \frac{91}{x} and \frac{-7xx}{x} have the same denominator, add them by adding their numerators.

$$\frac{91-7xx}{x}=0$$

Do the multiplications in 91-7xx.

$$\frac{91-7x^{2}}{x}=0$$

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

$$91-7x^{2}=0$$

Subtract 91 from both sides. Anything subtracted from zero gives its negation.

$$-7x^{2}=-91$$

Divide both sides by -7.

$$x^{2}=\frac{-91}{-7}$$

Divide -91 by -7 to get 13.

$$x^{2}=13$$

Take the square root of both sides of the equation.

$$x=\sqrt{13} x=-\sqrt{13}$$

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.

$$13\times \frac{7}{x}=7x$$

Express 13\times \frac{7}{x} as a single fraction.

$$\frac{13\times 7}{x}=7x$$

Multiply 13 and 7 to get 91.

$$\frac{91}{x}=7x$$

Subtract 7x from both sides.

$$\frac{91}{x}-7x=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -7x times \frac{x}{x}.

$$\frac{91}{x}+\frac{-7xx}{x}=0$$

Since \frac{91}{x} and \frac{-7xx}{x} have the same denominator, add them by adding their numerators.

$$\frac{91-7xx}{x}=0$$

Do the multiplications in 91-7xx.

$$\frac{91-7x^{2}}{x}=0$$

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

$$91-7x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-7x^{2}+91=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -7 for a, 0 for b, and 91 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-7\right)\times 91}}{2\left(-7\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-7\right)\times 91}}{2\left(-7\right)}$$

Multiply -4 times -7.

$$x=\frac{0±\sqrt{28\times 91}}{2\left(-7\right)}$$

Multiply 28 times 91.

$$x=\frac{0±\sqrt{2548}}{2\left(-7\right)}$$

Take the square root of 2548.

$$x=\frac{0±14\sqrt{13}}{2\left(-7\right)}$$

Multiply 2 times -7.

$$x=\frac{0±14\sqrt{13}}{-14}$$

Now solve the equation x=\frac{0±14\sqrt{13}}{-14} when ± is plus.

$$x=-\sqrt{13}$$

Now solve the equation x=\frac{0±14\sqrt{13}}{-14} when ± is minus.

$$x=\sqrt{13}$$

The equation is now solved.

$$x=-\sqrt{13} x=\sqrt{13}$$