Solve (x/6+5)^2-(x/6-5)^2=20

$$( \frac { x } { 6 } + 5 ) ^ { 2 } - ( \frac { x } { 6 } - 5 ) ^ { 2 } = 20$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{x}{6}+5\right)^{2}.

$$\left(\frac{x}{6}\right)^{2}+10\times \frac{x}{6}+25-\left(\frac{x}{6}-5\right)^{2}=20$$

To raise \frac{x}{6} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{x^{2}}{6^{2}}+10\times \frac{x}{6}+25-\left(\frac{x}{6}-5\right)^{2}=20$$

Express 10\times \frac{x}{6} as a single fraction.

$$\frac{x^{2}}{6^{2}}+\frac{10x}{6}+25-\left(\frac{x}{6}-5\right)^{2}=20$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6^{2} and 6 is 36. Multiply \frac{10x}{6} times \frac{6}{6}.

$$\frac{x^{2}}{36}+\frac{6\times 10x}{36}+25-\left(\frac{x}{6}-5\right)^{2}=20$$

Since \frac{x^{2}}{36} and \frac{6\times 10x}{36} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+6\times 10x}{36}+25-\left(\frac{x}{6}-5\right)^{2}=20$$

Do the multiplications in x^{2}+6\times 10x.

$$\frac{x^{2}+60x}{36}+25-\left(\frac{x}{6}-5\right)^{2}=20$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{x}{6}-5\right)^{2}.

$$\frac{x^{2}+60x}{36}+25-\left(\left(\frac{x}{6}\right)^{2}-10\times \frac{x}{6}+25\right)=20$$

To raise \frac{x}{6} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{x^{2}+60x}{36}+25-\left(\frac{x^{2}}{6^{2}}-10\times \frac{x}{6}+25\right)=20$$

Express -10\times \frac{x}{6} as a single fraction.

$$\frac{x^{2}+60x}{36}+25-\left(\frac{x^{2}}{6^{2}}+\frac{-10x}{6}+25\right)=20$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6^{2} and 6 is 36. Multiply \frac{-10x}{6} times \frac{6}{6}.

$$\frac{x^{2}+60x}{36}+25-\left(\frac{x^{2}}{36}+\frac{6\left(-1\right)\times 10x}{36}+25\right)=20$$

Since \frac{x^{2}}{36} and \frac{6\left(-1\right)\times 10x}{36} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+60x}{36}+25-\left(\frac{x^{2}+6\left(-1\right)\times 10x}{36}+25\right)=20$$

Do the multiplications in x^{2}+6\left(-1\right)\times 10x.

$$\frac{x^{2}+60x}{36}+25-\left(\frac{x^{2}-60x}{36}+25\right)=20$$

To find the opposite of \frac{x^{2}-60x}{36}+25, find the opposite of each term.

$$\frac{x^{2}+60x}{36}+25-\frac{x^{2}-60x}{36}-25=20$$

Subtract 25 from 25 to get 0.

$$\frac{x^{2}+60x}{36}-\frac{x^{2}-60x}{36}=20$$

Since \frac{x^{2}+60x}{36} and \frac{x^{2}-60x}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}+60x-\left(x^{2}-60x\right)}{36}=20$$

Do the multiplications in x^{2}+60x-\left(x^{2}-60x\right).

$$\frac{x^{2}+60x-x^{2}+60x}{36}=20$$

Combine like terms in x^{2}+60x-x^{2}+60x.

$$\frac{120x}{36}=20$$

Divide 120x by 36 to get \frac{10}{3}x.

$$\frac{10}{3}x=20$$

Multiply both sides by \frac{3}{10}, the reciprocal of \frac{10}{3}.

$$x=20\times \frac{3}{10}$$

Multiply 20 and \frac{3}{10} to get 6.

$$x=6$$