Solve x^2+16^2=(12+x)^2

$$x ^ { 2 } + 16 ^ { 2 } = ( 12 + x ) ^ { 2 }$$

Solve for x

$$x = \frac{14}{3} = 4\frac{2}{3} \approx 4.666666667$$

Steps for Solving Linear Equation

Calculate 16 to the power of 2 and get 256.

$$x^{2}+256=\left(12+x\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(12+x\right)^{2}.

$$x^{2}+256=144+24x+x^{2}$$

Subtract 24x from both sides.

$$x^{2}+256-24x=144+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+256-24x-x^{2}=144$$

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

$$256-24x=144$$

Subtract 256 from both sides.

$$-24x=144-256$$

Subtract 256 from 144 to get -112.

$$-24x=-112$$

Divide both sides by -24.

$$x=\frac{-112}{-24}$$

Reduce the fraction \frac{-112}{-24} to lowest terms by extracting and canceling out -8.

$$x=\frac{14}{3}$$