Solve 10^2+(x-4)^2=x^2

$$10 ^ { 2 } + ( x - 4 ) ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x = \frac{29}{2} = 14\frac{1}{2} = 14.5$$

Steps for Solving Linear Equation

Calculate 10 to the power of 2 and get 100.

$$100+\left(x-4\right)^{2}=x^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$100+x^{2}-8x+16=x^{2}$$

Add 100 and 16 to get 116.

$$116+x^{2}-8x=x^{2}$$

Subtract x^{2} from both sides.

$$116+x^{2}-8x-x^{2}=0$$

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

$$116-8x=0$$

Subtract 116 from both sides. Anything subtracted from zero gives its negation.

$$-8x=-116$$

Divide both sides by -8.

$$x=\frac{-116}{-8}$$

Reduce the fraction \frac{-116}{-8} to lowest terms by extracting and canceling out -4.

$$x=\frac{29}{2}$$