Solve 8.99*10^{9}*(2.5*7.2)*(10^-6)^2*(1/0.8-1/x)=1/21.7*10^-3(0-22^2)

$$8.99 \times 10 ^ { 9 } \times ( 2.5 \times 7.2 ) \times ( 10 ^ { - 6 } ) ^ { 2 } \times ( \frac { 1 } { 0.8 } - \frac { 1 } { x } ) = \frac { 1 } { 2 } 1.7 \times 10 ^ { - 3 } ( 0 - 22 ^ { 2 } )$$

Solve for x

$$x=\frac{32364}{122735}\approx 0.263690064$$

Steps Using Factoring

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.

$$8.99\times 10^{9}\times 2.5\times 7.2\times \left(10^{-6}\right)^{2}\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

To raise a power to another power, multiply the exponents. Multiply -6 and 2 to get -12.

$$8.99\times 10^{9}\times 2.5\times 7.2\times 10^{-12}\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

To multiply powers of the same base, add their exponents. Add 9 and -12 to get -3.

$$8.99\times 10^{-3}\times 2.5\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$8.99\times \frac{1}{1000}\times 2.5\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply 8.99 and \frac{1}{1000} to get \frac{899}{100000}.

$$\frac{899}{100000}\times 2.5\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{899}{100000} and 2.5 to get \frac{899}{40000}.

$$\frac{899}{40000}\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{899}{40000} and 7.2 to get \frac{8091}{50000}.

$$\frac{8091}{50000}\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Expand \frac{1}{0.8} by multiplying both numerator and the denominator by 10.

$$\frac{8091}{50000}\left(\frac{10}{8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{8091}{50000}\left(\frac{5}{4}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{5}{4} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{4}{4}.

$$\frac{8091}{50000}\left(\frac{5x}{4x}-\frac{4}{4x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Since \frac{5x}{4x} and \frac{4}{4x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8091}{50000}\times \frac{5x-4}{4x}\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{8091}{50000} and 2 to get \frac{8091}{25000}.

$$\frac{8091}{25000}\times \frac{5x-4}{4x}x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{8091}{25000} times \frac{5x-4}{4x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8091\left(5x-4\right)}{25000\times 4x}x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Express \frac{8091\left(5x-4\right)}{25000\times 4x}x as a single fraction.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{1}{2} and 1.7 to get \frac{17}{20}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20}\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20}\times \frac{1}{1000}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{17}{20} and \frac{1}{1000} to get \frac{17}{20000}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20000}\left(0-22^{2}\right)\times 2x$$

Calculate 22 to the power of 2 and get 484.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20000}\left(0-484\right)\times 2x$$

Subtract 484 from 0 to get -484.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20000}\left(-484\right)\times 2x$$

Multiply \frac{17}{20000} and -484 to get -\frac{2057}{5000}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=-\frac{2057}{5000}\times 2x$$

Multiply -\frac{2057}{5000} and 2 to get -\frac{2057}{2500}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=-\frac{2057}{2500}x$$

Multiply 25000 and 4 to get 100000.

$$\frac{8091\left(5x-4\right)x}{100000x}=-\frac{2057}{2500}x$$

Add \frac{2057}{2500}x to both sides.

$$\frac{8091\left(5x-4\right)x}{100000x}+\frac{2057}{2500}x=0$$

Use the distributive property to multiply 8091 by 5x-4.

$$\frac{\left(40455x-32364\right)x}{100000x}+\frac{2057}{2500}x=0$$

Use the distributive property to multiply 40455x-32364 by x.

$$\frac{40455x^{2}-32364x}{100000x}+\frac{2057}{2500}x=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100000x, the least common multiple of 100000x,2500.

$$40455x^{2}-32364x+\frac{2057}{2500}x\times 100000x=0$$

Reorder the terms.

$$40455x^{2}+\frac{2057}{2500}\times 100000xx-32364x=0$$

Multiply x and x to get x^{2}.

$$40455x^{2}+\frac{2057}{2500}\times 100000x^{2}-32364x=0$$

Multiply \frac{2057}{2500} and 100000 to get 82280.

$$40455x^{2}+82280x^{2}-32364x=0$$

Combine 40455x^{2} and 82280x^{2} to get 122735x^{2}.

$$122735x^{2}-32364x=0$$

Factor out x.

$$x\left(122735x-32364\right)=0$$

To find equation solutions, solve x=0 and 122735x-32364=0.

$$x=0 x=\frac{32364}{122735}$$

Variable x cannot be equal to 0.

$$x=\frac{32364}{122735}$$

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 2x, the least common multiple of x,2.

$$8.99\times 10^{9}\times 2.5\times 7.2\times \left(10^{-6}\right)^{2}\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

To raise a power to another power, multiply the exponents. Multiply -6 and 2 to get -12.

$$8.99\times 10^{9}\times 2.5\times 7.2\times 10^{-12}\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

To multiply powers of the same base, add their exponents. Add 9 and -12 to get -3.

$$8.99\times 10^{-3}\times 2.5\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$8.99\times \frac{1}{1000}\times 2.5\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply 8.99 and \frac{1}{1000} to get \frac{899}{100000}.

$$\frac{899}{100000}\times 2.5\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{899}{100000} and 2.5 to get \frac{899}{40000}.

$$\frac{899}{40000}\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{899}{40000} and 7.2 to get \frac{8091}{50000}.

$$\frac{8091}{50000}\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Expand \frac{1}{0.8} by multiplying both numerator and the denominator by 10.

$$\frac{8091}{50000}\left(\frac{10}{8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{8091}{50000}\left(\frac{5}{4}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{5}{4} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{4}{4}.

$$\frac{8091}{50000}\left(\frac{5x}{4x}-\frac{4}{4x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Since \frac{5x}{4x} and \frac{4}{4x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8091}{50000}\times \frac{5x-4}{4x}\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{8091}{50000} and 2 to get \frac{8091}{25000}.

$$\frac{8091}{25000}\times \frac{5x-4}{4x}x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{8091}{25000} times \frac{5x-4}{4x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8091\left(5x-4\right)}{25000\times 4x}x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Express \frac{8091\left(5x-4\right)}{25000\times 4x}x as a single fraction.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{1}{2} and 1.7 to get \frac{17}{20}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20}\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20}\times \frac{1}{1000}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{17}{20} and \frac{1}{1000} to get \frac{17}{20000}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20000}\left(0-22^{2}\right)\times 2x$$

Calculate 22 to the power of 2 and get 484.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20000}\left(0-484\right)\times 2x$$

Subtract 484 from 0 to get -484.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20000}\left(-484\right)\times 2x$$

Multiply \frac{17}{20000} and -484 to get -\frac{2057}{5000}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=-\frac{2057}{5000}\times 2x$$

Multiply -\frac{2057}{5000} and 2 to get -\frac{2057}{2500}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=-\frac{2057}{2500}x$$

Multiply 25000 and 4 to get 100000.

$$\frac{8091\left(5x-4\right)x}{100000x}=-\frac{2057}{2500}x$$

Add \frac{2057}{2500}x to both sides.

$$\frac{8091\left(5x-4\right)x}{100000x}+\frac{2057}{2500}x=0$$

Use the distributive property to multiply 8091 by 5x-4.

$$\frac{\left(40455x-32364\right)x}{100000x}+\frac{2057}{2500}x=0$$

Use the distributive property to multiply 40455x-32364 by x.

$$\frac{40455x^{2}-32364x}{100000x}+\frac{2057}{2500}x=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100000x, the least common multiple of 100000x,2500.

$$40455x^{2}-32364x+\frac{2057}{2500}x\times 100000x=0$$

Reorder the terms.

$$40455x^{2}+\frac{2057}{2500}\times 100000xx-32364x=0$$

Multiply x and x to get x^{2}.

$$40455x^{2}+\frac{2057}{2500}\times 100000x^{2}-32364x=0$$

Multiply \frac{2057}{2500} and 100000 to get 82280.

$$40455x^{2}+82280x^{2}-32364x=0$$

Combine 40455x^{2} and 82280x^{2} to get 122735x^{2}.

$$122735x^{2}-32364x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 122735 for a, -32364 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-32364\right)±\sqrt{\left(-32364\right)^{2}}}{2\times 122735}$$

Take the square root of \left(-32364\right)^{2}.

$$x=\frac{-\left(-32364\right)±32364}{2\times 122735}$$

The opposite of -32364 is 32364.

$$x=\frac{32364±32364}{2\times 122735}$$

Multiply 2 times 122735.

$$x=\frac{32364±32364}{245470}$$

Now solve the equation x=\frac{32364±32364}{245470} when ± is plus. Add 32364 to 32364.

$$x=\frac{64728}{245470}$$

Reduce the fraction \frac{64728}{245470} to lowest terms by extracting and canceling out 2.

$$x=\frac{32364}{122735}$$

Now solve the equation x=\frac{32364±32364}{245470} when ± is minus. Subtract 32364 from 32364.

$$x=\frac{0}{245470}$$

Divide 0 by 245470.

$$x=0$$

The equation is now solved.

$$x=\frac{32364}{122735} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{32364}{122735}$$

Steps for Completing the Square

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.

$$8.99\times 10^{9}\times 2.5\times 7.2\times \left(10^{-6}\right)^{2}\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

To raise a power to another power, multiply the exponents. Multiply -6 and 2 to get -12.

$$8.99\times 10^{9}\times 2.5\times 7.2\times 10^{-12}\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

To multiply powers of the same base, add their exponents. Add 9 and -12 to get -3.

$$8.99\times 10^{-3}\times 2.5\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$8.99\times \frac{1}{1000}\times 2.5\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply 8.99 and \frac{1}{1000} to get \frac{899}{100000}.

$$\frac{899}{100000}\times 2.5\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{899}{100000} and 2.5 to get \frac{899}{40000}.

$$\frac{899}{40000}\times 7.2\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{899}{40000} and 7.2 to get \frac{8091}{50000}.

$$\frac{8091}{50000}\left(\frac{1}{0.8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Expand \frac{1}{0.8} by multiplying both numerator and the denominator by 10.

$$\frac{8091}{50000}\left(\frac{10}{8}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{8091}{50000}\left(\frac{5}{4}-\frac{1}{x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{5}{4} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{4}{4}.

$$\frac{8091}{50000}\left(\frac{5x}{4x}-\frac{4}{4x}\right)\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Since \frac{5x}{4x} and \frac{4}{4x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8091}{50000}\times \frac{5x-4}{4x}\times 2x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{8091}{50000} and 2 to get \frac{8091}{25000}.

$$\frac{8091}{25000}\times \frac{5x-4}{4x}x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{8091}{25000} times \frac{5x-4}{4x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8091\left(5x-4\right)}{25000\times 4x}x=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Express \frac{8091\left(5x-4\right)}{25000\times 4x}x as a single fraction.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{1}{2}\times 1.7\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{1}{2} and 1.7 to get \frac{17}{20}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20}\times 10^{-3}\left(0-22^{2}\right)\times 2x$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20}\times \frac{1}{1000}\left(0-22^{2}\right)\times 2x$$

Multiply \frac{17}{20} and \frac{1}{1000} to get \frac{17}{20000}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20000}\left(0-22^{2}\right)\times 2x$$

Calculate 22 to the power of 2 and get 484.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20000}\left(0-484\right)\times 2x$$

Subtract 484 from 0 to get -484.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=\frac{17}{20000}\left(-484\right)\times 2x$$

Multiply \frac{17}{20000} and -484 to get -\frac{2057}{5000}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=-\frac{2057}{5000}\times 2x$$

Multiply -\frac{2057}{5000} and 2 to get -\frac{2057}{2500}.

$$\frac{8091\left(5x-4\right)x}{25000\times 4x}=-\frac{2057}{2500}x$$

Multiply 25000 and 4 to get 100000.

$$\frac{8091\left(5x-4\right)x}{100000x}=-\frac{2057}{2500}x$$

Add \frac{2057}{2500}x to both sides.

$$\frac{8091\left(5x-4\right)x}{100000x}+\frac{2057}{2500}x=0$$

Use the distributive property to multiply 8091 by 5x-4.

$$\frac{\left(40455x-32364\right)x}{100000x}+\frac{2057}{2500}x=0$$

Use the distributive property to multiply 40455x-32364 by x.

$$\frac{40455x^{2}-32364x}{100000x}+\frac{2057}{2500}x=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100000x, the least common multiple of 100000x,2500.

$$40455x^{2}-32364x+\frac{2057}{2500}x\times 100000x=0$$

Reorder the terms.

$$40455x^{2}+\frac{2057}{2500}\times 100000xx-32364x=0$$

Multiply x and x to get x^{2}.

$$40455x^{2}+\frac{2057}{2500}\times 100000x^{2}-32364x=0$$

Multiply \frac{2057}{2500} and 100000 to get 82280.

$$40455x^{2}+82280x^{2}-32364x=0$$

Combine 40455x^{2} and 82280x^{2} to get 122735x^{2}.

$$122735x^{2}-32364x=0$$

Divide both sides by 122735.

$$\frac{122735x^{2}-32364x}{122735}=\frac{0}{122735}$$

Dividing by 122735 undoes the multiplication by 122735.

$$x^{2}-\frac{32364}{122735}x=\frac{0}{122735}$$

Divide 0 by 122735.

$$x^{2}-\frac{32364}{122735}x=0$$

Divide -\frac{32364}{122735}, the coefficient of the x term, by 2 to get -\frac{16182}{122735}. Then add the square of -\frac{16182}{122735} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{32364}{122735}x+\left(-\frac{16182}{122735}\right)^{2}=\left(-\frac{16182}{122735}\right)^{2}$$

Square -\frac{16182}{122735} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{32364}{122735}x+\frac{261857124}{15063880225}=\frac{261857124}{15063880225}$$

Factor x^{2}-\frac{32364}{122735}x+\frac{261857124}{15063880225}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{16182}{122735}\right)^{2}=\frac{261857124}{15063880225}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{16182}{122735}\right)^{2}}=\sqrt{\frac{261857124}{15063880225}}$$

Simplify.

$$x-\frac{16182}{122735}=\frac{16182}{122735} x-\frac{16182}{122735}=-\frac{16182}{122735}$$

Add \frac{16182}{122735} to both sides of the equation.

$$x=\frac{32364}{122735} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{32364}{122735}$$