Solve 12^2-x^2=16^2-left(20-xright)^2

$${ 12 }^{ 2 } - { x }^{ 2 } = { 16 }^{ 2 } - { \left(20-x \right) }^{ 2 }$$

Solve for x

$$x = \frac{36}{5} = 7\frac{1}{5} = 7.2$$

Steps for Solving Linear Equation

Calculate 12 to the power of 2 and get 144.

$$144-x^{2}=16^{2}-\left(20-x\right)^{2}$$

Calculate 16 to the power of 2 and get 256.

$$144-x^{2}=256-\left(20-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(20-x\right)^{2}.

$$144-x^{2}=256-\left(400-40x+x^{2}\right)$$

To find the opposite of 400-40x+x^{2}, find the opposite of each term.

$$144-x^{2}=256-400+40x-x^{2}$$

Subtract 400 from 256 to get -144.

$$144-x^{2}=-144+40x-x^{2}$$

Subtract 40x from both sides.

$$144-x^{2}-40x=-144-x^{2}$$

Add x^{2} to both sides.

$$144-x^{2}-40x+x^{2}=-144$$

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

$$144-40x=-144$$

Subtract 144 from both sides.

$$-40x=-144-144$$

Subtract 144 from -144 to get -288.

$$-40x=-288$$

Divide both sides by -40.

$$x=\frac{-288}{-40}$$

Reduce the fraction \frac{-288}{-40} to lowest terms by extracting and canceling out -8.

$$x=\frac{36}{5}$$