Solve left(12-xright)^2+8^2=x^2

$${ \left(12-x \right) }^{ 2 } + { 8 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x = \frac{26}{3} = 8\frac{2}{3} \approx 8.666666667$$

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}.

$$144-24x+x^{2}+8^{2}=x^{2}$$

Calculate 8 to the power of 2 and get 64.

$$144-24x+x^{2}+64=x^{2}$$

Add 144 and 64 to get 208.

$$208-24x+x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$208-24x+x^{2}-x^{2}=0$$

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

$$208-24x=0$$

Subtract 208 from both sides. Anything subtracted from zero gives its negation.

$$-24x=-208$$

Divide both sides by -24.

$$x=\frac{-208}{-24}$$

Reduce the fraction \frac{-208}{-24} to lowest terms by extracting and canceling out -8.

$$x=\frac{26}{3}$$