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

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

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}.

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

Calculate 16 to the power of 2 and get 256.

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

Add 144 and 256 to get 400.

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

Subtract x^{2} from both sides.

$$x^{2}-24x+400-x^{2}=0$$

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

$$-24x+400=0$$

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.

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