Solve 10^2-x^2=13^2-left(13-xright)^2

$${ 10 }^{ 2 } - { x }^{ 2 } = { 13 }^{ 2 } - { \left(13-x \right) }^{ 2 }$$

Solve for x

$$x = \frac{50}{13} = 3\frac{11}{13} \approx 3.846153846$$

Steps for Solving Linear Equation

Calculate 10 to the power of 2 and get 100.

$$100-x^{2}=13^{2}-\left(13-x\right)^{2}$$

Calculate 13 to the power of 2 and get 169.

$$100-x^{2}=169-\left(13-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(13-x\right)^{2}.

$$100-x^{2}=169-\left(169-26x+x^{2}\right)$$

To find the opposite of 169-26x+x^{2}, find the opposite of each term.

$$100-x^{2}=169-169+26x-x^{2}$$

Subtract 169 from 169 to get 0.

$$100-x^{2}=26x-x^{2}$$

Subtract 26x from both sides.

$$100-x^{2}-26x=-x^{2}$$

Add x^{2} to both sides.

$$100-x^{2}-26x+x^{2}=0$$

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

$$100-26x=0$$

Subtract 100 from both sides. Anything subtracted from zero gives its negation.

$$-26x=-100$$

Divide both sides by -26.

$$x=\frac{-100}{-26}$$

Reduce the fraction \frac{-100}{-26} to lowest terms by extracting and canceling out -2.

$$x=\frac{50}{13}$$