Solve 1/5[(98-90)^{2}+(918-90)^2+(91-90)^2+(183-90)^2+(80-90)^2]

$$\frac { 1 } { 5 } [ ( 98 - 90 ) ^ { 2 } + ( 918 - 90 ) ^ { 2 } + ( 91 - 90 ) ^ { 2 } + ( 183 - 90 ) ^ { 2 } + ( 80 - 90 ) ^ { 2 } ]$$

Evaluate

$$\frac{694398}{5}=138879.6$$

Solution Steps

Subtract 90 from 98 to get 8.

$$\frac{1}{5}\left(8^{2}+\left(918-90\right)^{2}+\left(91-90\right)^{2}+\left(183-90\right)^{2}+\left(80-90\right)^{2}\right)$$

Calculate 8 to the power of 2 and get 64.

$$\frac{1}{5}\left(64+\left(918-90\right)^{2}+\left(91-90\right)^{2}+\left(183-90\right)^{2}+\left(80-90\right)^{2}\right)$$

Subtract 90 from 918 to get 828.

$$\frac{1}{5}\left(64+828^{2}+\left(91-90\right)^{2}+\left(183-90\right)^{2}+\left(80-90\right)^{2}\right)$$

Calculate 828 to the power of 2 and get 685584.

$$\frac{1}{5}\left(64+685584+\left(91-90\right)^{2}+\left(183-90\right)^{2}+\left(80-90\right)^{2}\right)$$

Add 64 and 685584 to get 685648.

$$\frac{1}{5}\left(685648+\left(91-90\right)^{2}+\left(183-90\right)^{2}+\left(80-90\right)^{2}\right)$$

Subtract 90 from 91 to get 1.

$$\frac{1}{5}\left(685648+1^{2}+\left(183-90\right)^{2}+\left(80-90\right)^{2}\right)$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{5}\left(685648+1+\left(183-90\right)^{2}+\left(80-90\right)^{2}\right)$$

Add 685648 and 1 to get 685649.

$$\frac{1}{5}\left(685649+\left(183-90\right)^{2}+\left(80-90\right)^{2}\right)$$

Subtract 90 from 183 to get 93.

$$\frac{1}{5}\left(685649+93^{2}+\left(80-90\right)^{2}\right)$$

Calculate 93 to the power of 2 and get 8649.

$$\frac{1}{5}\left(685649+8649+\left(80-90\right)^{2}\right)$$

Add 685649 and 8649 to get 694298.

$$\frac{1}{5}\left(694298+\left(80-90\right)^{2}\right)$$

Subtract 90 from 80 to get -10.

$$\frac{1}{5}\left(694298+\left(-10\right)^{2}\right)$$

Calculate -10 to the power of 2 and get 100.

$$\frac{1}{5}\left(694298+100\right)$$

Add 694298 and 100 to get 694398.

$$\frac{1}{5}\times 694398$$

Multiply \frac{1}{5} and 694398 to get \frac{694398}{5}.

$$\frac{694398}{5}$$

Factor

$$\frac{2 \cdot 3 \cdot 115733}{5} = 138879\frac{3}{5} = 138879.6$$