Solve x^2=10^2+(x-12)^2

$$x ^ { 2 } = 10 ^ { 2 } + ( x - 12 ) ^ { 2 }$$

Solve for x

$$x = \frac{61}{6} = 10\frac{1}{6} \approx 10.166666667$$

Steps for Solving Linear Equation

Calculate 10 to the power of 2 and get 100.

$$x^{2}=100+\left(x-12\right)^{2}$$

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

$$x^{2}=100+x^{2}-24x+144$$

Add 100 and 144 to get 244.

$$x^{2}=244+x^{2}-24x$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=244-24x$$

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

$$0=244-24x$$

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

$$244-24x=0$$

Subtract 244 from both sides. Anything subtracted from zero gives its negation.

$$-24x=-244$$

Divide both sides by -24.

$$x=\frac{-244}{-24}$$

Reduce the fraction \frac{-244}{-24} to lowest terms by extracting and canceling out -4.

$$x=\frac{61}{6}$$