Solve A/2n^{2}=11^2-107^2+96^2+59^2

$$\frac { A } { 2 } n ^ { 2 } = 11 ^ { 2 } - 107 ^ { 2 } + 96 ^ { 2 } + 59 ^ { 2 }$$

Solve for A

$$A=\frac{2738}{n^{2}}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$An^{2}=2\left(11^{2}-107^{2}\right)+2\times 96^{2}+2\times 59^{2}$$

Calculate 11 to the power of 2 and get 121.

$$An^{2}=2\left(121-107^{2}\right)+2\times 96^{2}+2\times 59^{2}$$

Calculate 107 to the power of 2 and get 11449.

$$An^{2}=2\left(121-11449\right)+2\times 96^{2}+2\times 59^{2}$$

Subtract 11449 from 121 to get -11328.

$$An^{2}=2\left(-11328\right)+2\times 96^{2}+2\times 59^{2}$$

Multiply 2 and -11328 to get -22656.

$$An^{2}=-22656+2\times 96^{2}+2\times 59^{2}$$

Calculate 96 to the power of 2 and get 9216.

$$An^{2}=-22656+2\times 9216+2\times 59^{2}$$

Multiply 2 and 9216 to get 18432.

$$An^{2}=-22656+18432+2\times 59^{2}$$

Add -22656 and 18432 to get -4224.

$$An^{2}=-4224+2\times 59^{2}$$

Calculate 59 to the power of 2 and get 3481.

$$An^{2}=-4224+2\times 3481$$

Multiply 2 and 3481 to get 6962.

$$An^{2}=-4224+6962$$

Add -4224 and 6962 to get 2738.

$$An^{2}=2738$$

The equation is in standard form.

$$n^{2}A=2738$$

Divide both sides by n^{2}.

$$\frac{n^{2}A}{n^{2}}=\frac{2738}{n^{2}}$$

Dividing by n^{2} undoes the multiplication by n^{2}.

$$A=\frac{2738}{n^{2}}$$

Solve for n

$$n=37\sqrt{\frac{2}{A}}$$

$$n=-37\sqrt{\frac{2}{A}}\text{, }A>0$$