Solve 16^2-(10+x)^2=10^2-x^2

$$16 ^ { 2 } - ( 10 + x ) ^ { 2 } = 10 ^ { 2 } - x ^ { 2 }$$

Solve for x

$$x = \frac{14}{5} = 2\frac{4}{5} = 2.8$$

Steps for Solving Linear Equation

Calculate 16 to the power of 2 and get 256.

$$256-\left(10+x\right)^{2}=10^{2}-x^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(10+x\right)^{2}.

$$256-\left(100+20x+x^{2}\right)=10^{2}-x^{2}$$

To find the opposite of 100+20x+x^{2}, find the opposite of each term.

$$256-100-20x-x^{2}=10^{2}-x^{2}$$

Subtract 100 from 256 to get 156.

$$156-20x-x^{2}=10^{2}-x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$156-20x-x^{2}=100-x^{2}$$

Add x^{2} to both sides.

$$156-20x-x^{2}+x^{2}=100$$

Combine -x^{2} and x^{2} to get 0.

$$156-20x=100$$

Subtract 156 from both sides.

$$-20x=100-156$$

Subtract 156 from 100 to get -56.

$$-20x=-56$$

Divide both sides by -20.

$$x=\frac{-56}{-20}$$

Reduce the fraction \frac{-56}{-20} to lowest terms by extracting and canceling out -4.

$$x=\frac{14}{5}$$