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

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

Solve for x

$$x = \frac{16}{3} = 5\frac{1}{3} \approx 5.333333333$$

Steps for Solving Linear Equation

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

$$16+x^{2}=144-24x+x^{2}$$

Add 24x to both sides.

$$16+x^{2}+24x=144+x^{2}$$

Subtract x^{2} from both sides.

$$16+x^{2}+24x-x^{2}=144$$

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

$$16+24x=144$$

Subtract 16 from both sides.

$$24x=144-16$$

Subtract 16 from 144 to get 128.

$$24x=128$$

Divide both sides by 24.

$$x=\frac{128}{24}$$

Reduce the fraction \frac{128}{24} to lowest terms by extracting and canceling out 8.

$$x=\frac{16}{3}$$