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

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

Solve for x

$$x = \frac{50}{3} = 16\frac{2}{3} \approx 16.666666667$$

Steps for Solving Linear Equation

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

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

Calculate 16 to the power of 2 and get 256.

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

Add 144 and 256 to get 400.

$$x^{2}=x^{2}-24x+400$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=-24x+400$$

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

$$0=-24x+400$$

Swap sides so that all variable terms are on the left hand side.

$$-24x+400=0$$

Subtract 400 from both sides. Anything subtracted from zero gives its negation.

$$-24x=-400$$

Divide both sides by -24.

$$x=\frac{-400}{-24}$$

Reduce the fraction \frac{-400}{-24} to lowest terms by extracting and canceling out -8.

$$x=\frac{50}{3}$$