Solve 1.096776*10^7*(1/5^2-1/6^2)=1/x

$$1.096776 \times { 10 }^{ 7 } \times ( \frac{ 1 }{ { 5 }^{ 2 } } - \frac{ 1 }{ { 6 }^{ 2 } } )= \frac{ 1 }{ x }$$

Solve for x

$$x=\frac{5}{670252}\approx 0.00000746$$

Steps for Solving Linear Equation

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

$$1.096776\times 10^{7}\left(\frac{1}{5^{2}}-\frac{1}{6^{2}}\right)x=1$$

Calculate 10 to the power of 7 and get 10000000.

$$1.096776\times 10000000\left(\frac{1}{5^{2}}-\frac{1}{6^{2}}\right)x=1$$

Multiply 1.096776 and 10000000 to get 10967760.

$$10967760\left(\frac{1}{5^{2}}-\frac{1}{6^{2}}\right)x=1$$

Calculate 5 to the power of 2 and get 25.

$$10967760\left(\frac{1}{25}-\frac{1}{6^{2}}\right)x=1$$

Calculate 6 to the power of 2 and get 36.

$$10967760\left(\frac{1}{25}-\frac{1}{36}\right)x=1$$

Least common multiple of 25 and 36 is 900. Convert \frac{1}{25} and \frac{1}{36} to fractions with denominator 900.

$$10967760\left(\frac{36}{900}-\frac{25}{900}\right)x=1$$

Since \frac{36}{900} and \frac{25}{900} have the same denominator, subtract them by subtracting their numerators.

$$10967760\times \frac{36-25}{900}x=1$$

Subtract 25 from 36 to get 11.

$$10967760\times \frac{11}{900}x=1$$

Express 10967760\times \frac{11}{900} as a single fraction.

$$\frac{10967760\times 11}{900}x=1$$

Multiply 10967760 and 11 to get 120645360.

$$\frac{120645360}{900}x=1$$

Reduce the fraction \frac{120645360}{900} to lowest terms by extracting and canceling out 180.

$$\frac{670252}{5}x=1$$

Multiply both sides by \frac{5}{670252}, the reciprocal of \frac{670252}{5}.

$$x=1\times \frac{5}{670252}$$

Multiply 1 and \frac{5}{670252} to get \frac{5}{670252}.

$$x=\frac{5}{670252}$$