Solve 8^2-(10-x)^2=6^2-x^2

$$8 ^ { 2 } - ( 10 - x ) ^ { 2 } = 6 ^ { 2 } - x ^ { 2 }$$

Solve for x

$$x = \frac{18}{5} = 3\frac{3}{5} = 3.6$$

Steps for Solving Linear Equation

Calculate 8 to the power of 2 and get 64.

$$64-\left(10-x\right)^{2}=6^{2}-x^{2}$$

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

$$64-\left(100-20x+x^{2}\right)=6^{2}-x^{2}$$

To find the opposite of 100-20x+x^{2}, find the opposite of each term.

$$64-100+20x-x^{2}=6^{2}-x^{2}$$

Subtract 100 from 64 to get -36.

$$-36+20x-x^{2}=6^{2}-x^{2}$$

Calculate 6 to the power of 2 and get 36.

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

Add x^{2} to both sides.

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

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

$$-36+20x=36$$

Add 36 to both sides.

$$20x=36+36$$

Add 36 and 36 to get 72.

$$20x=72$$

Divide both sides by 20.

$$x=\frac{72}{20}$$

Reduce the fraction \frac{72}{20} to lowest terms by extracting and canceling out 4.

$$x=\frac{18}{5}$$