Solve 10^2-x^2=8^2-left(12-xright)^2

$${ 10 }^{ 2 } - { x }^{ 2 } = { 8 }^{ 2 } - { \left(12-x \right) }^{ 2 }$$

Solve for x

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Steps for Solving Linear Equation

Calculate 10 to the power of 2 and get 100.

$$100-x^{2}=8^{2}-\left(12-x\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$100-x^{2}=64-\left(12-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(12-x\right)^{2}.

$$100-x^{2}=64-\left(144-24x+x^{2}\right)$$

To find the opposite of 144-24x+x^{2}, find the opposite of each term.

$$100-x^{2}=64-144+24x-x^{2}$$

Subtract 144 from 64 to get -80.

$$100-x^{2}=-80+24x-x^{2}$$

Subtract 24x from both sides.

$$100-x^{2}-24x=-80-x^{2}$$

Add x^{2} to both sides.

$$100-x^{2}-24x+x^{2}=-80$$

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

$$100-24x=-80$$

Subtract 100 from both sides.

$$-24x=-80-100$$

Subtract 100 from -80 to get -180.

$$-24x=-180$$

Divide both sides by -24.

$$x=\frac{-180}{-24}$$

Reduce the fraction \frac{-180}{-24} to lowest terms by extracting and canceling out -12.

$$x=\frac{15}{2}$$