Solve 13^2+x^2=left(169-xright)^2

$${ 13 }^{ 2 } + { x }^{ 2 } = { \left(169-x \right) }^{ 2 }$$

Solve for x

$$x=84$$

Steps for Solving Linear Equation

Calculate 13 to the power of 2 and get 169.

$$169+x^{2}=\left(169-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(169-x\right)^{2}.

$$169+x^{2}=28561-338x+x^{2}$$

Add 338x to both sides.

$$169+x^{2}+338x=28561+x^{2}$$

Subtract x^{2} from both sides.

$$169+x^{2}+338x-x^{2}=28561$$

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

$$169+338x=28561$$

Subtract 169 from both sides.

$$338x=28561-169$$

Subtract 169 from 28561 to get 28392.

$$338x=28392$$

Divide both sides by 338.

$$x=\frac{28392}{338}$$

Divide 28392 by 338 to get 84.

$$x=84$$