Solve x^2+6^2=left(10-xright)^2

$${ x }^{ 2 } + { 6 }^{ 2 } = { \left(10-x \right) }^{ 2 }$$

Solve for x

$$x = \frac{16}{5} = 3\frac{1}{5} = 3.2$$

Steps for Solving Linear Equation

Calculate 6 to the power of 2 and get 36.

$$x^{2}+36=\left(10-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10-x\right)^{2}.

$$x^{2}+36=100-20x+x^{2}$$

Add 20x to both sides.

$$x^{2}+36+20x=100+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+36+20x-x^{2}=100$$

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

$$36+20x=100$$

Subtract 36 from both sides.

$$20x=100-36$$

Subtract 36 from 100 to get 64.

$$20x=64$$

Divide both sides by 20.

$$x=\frac{64}{20}$$

Reduce the fraction \frac{64}{20} to lowest terms by extracting and canceling out 4.

$$x=\frac{16}{5}$$