Solve 1/10left(left(9-83right)^2*2+left(8-83right)^2*6+left(10-83right)^2+left(7-83right)^2right)

$$\frac{ 1 }{ 10 } \left( { \left(9-83 \right) }^{ 2 } \times 2+ { \left(8-83 \right) }^{ 2 } \times 6+ { \left(10-83 \right) }^{ 2 } + { \left(7-83 \right) }^{ 2 } \right)$$

Evaluate

$$\frac{55807}{10}=5580.7$$

Solution Steps

Subtract 83 from 9 to get -74.

$$\frac{1}{10}\left(\left(-74\right)^{2}\times 2+\left(8-83\right)^{2}\times 6+\left(10-83\right)^{2}+\left(7-83\right)^{2}\right)$$

Calculate -74 to the power of 2 and get 5476.

$$\frac{1}{10}\left(5476\times 2+\left(8-83\right)^{2}\times 6+\left(10-83\right)^{2}+\left(7-83\right)^{2}\right)$$

Multiply 5476 and 2 to get 10952.

$$\frac{1}{10}\left(10952+\left(8-83\right)^{2}\times 6+\left(10-83\right)^{2}+\left(7-83\right)^{2}\right)$$

Subtract 83 from 8 to get -75.

$$\frac{1}{10}\left(10952+\left(-75\right)^{2}\times 6+\left(10-83\right)^{2}+\left(7-83\right)^{2}\right)$$

Calculate -75 to the power of 2 and get 5625.

$$\frac{1}{10}\left(10952+5625\times 6+\left(10-83\right)^{2}+\left(7-83\right)^{2}\right)$$

Multiply 5625 and 6 to get 33750.

$$\frac{1}{10}\left(10952+33750+\left(10-83\right)^{2}+\left(7-83\right)^{2}\right)$$

Add 10952 and 33750 to get 44702.

$$\frac{1}{10}\left(44702+\left(10-83\right)^{2}+\left(7-83\right)^{2}\right)$$

Subtract 83 from 10 to get -73.

$$\frac{1}{10}\left(44702+\left(-73\right)^{2}+\left(7-83\right)^{2}\right)$$

Calculate -73 to the power of 2 and get 5329.

$$\frac{1}{10}\left(44702+5329+\left(7-83\right)^{2}\right)$$

Add 44702 and 5329 to get 50031.

$$\frac{1}{10}\left(50031+\left(7-83\right)^{2}\right)$$

Subtract 83 from 7 to get -76.

$$\frac{1}{10}\left(50031+\left(-76\right)^{2}\right)$$

Calculate -76 to the power of 2 and get 5776.

$$\frac{1}{10}\left(50031+5776\right)$$

Add 50031 and 5776 to get 55807.

$$\frac{1}{10}\times 55807$$

Multiply \frac{1}{10} and 55807 to get \frac{55807}{10}.

$$\frac{55807}{10}$$

Factor

$$\frac{55807}{2 \cdot 5} = 5580\frac{7}{10} = 5580.7$$