Solve frac{left(6-8.5right)^2+left(6-8.5right)^2+left(9-8.5right)^2+left(9-8.5right)^2+{left(9-8.5right)}^2+{left(9-8.5right)}^2+{left(12-8.5right)}^2}{7}

$$\frac{ { \left(6-8.5 \right) }^{ 2 } + { \left(6-8.5 \right) }^{ 2 } + { \left(9-8.5 \right) }^{ 2 } + { \left(9-8.5 \right) }^{ 2 } + { \left(9-8.5 \right) }^{ 2 } + { \left(9-8.5 \right) }^{ 2 } + { \left(12-8.5 \right) }^{ 2 } }{ 7 }$$

Evaluate

$$\frac{103}{28}\approx 3.678571429$$

Solution Steps

Subtract 8.5 from 6 to get -2.5.

$$\frac{\left(-2.5\right)^{2}+\left(6-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Calculate -2.5 to the power of 2 and get 6.25.

$$\frac{6.25+\left(6-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Subtract 8.5 from 6 to get -2.5.

$$\frac{6.25+\left(-2.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Calculate -2.5 to the power of 2 and get 6.25.

$$\frac{6.25+6.25+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Add 6.25 and 6.25 to get 12.5.

$$\frac{12.5+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Subtract 8.5 from 9 to get 0.5.

$$\frac{12.5+0.5^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Calculate 0.5 to the power of 2 and get 0.25.

$$\frac{12.5+0.25+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Add 12.5 and 0.25 to get 12.75.

$$\frac{12.75+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Subtract 8.5 from 9 to get 0.5.

$$\frac{12.75+0.5^{2}+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Calculate 0.5 to the power of 2 and get 0.25.

$$\frac{12.75+0.25+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Add 12.75 and 0.25 to get 13.

$$\frac{13+\left(9-8.5\right)^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Subtract 8.5 from 9 to get 0.5.

$$\frac{13+0.5^{2}+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Calculate 0.5 to the power of 2 and get 0.25.

$$\frac{13+0.25+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Add 13 and 0.25 to get 13.25.

$$\frac{13.25+\left(9-8.5\right)^{2}+\left(12-8.5\right)^{2}}{7}$$

Subtract 8.5 from 9 to get 0.5.

$$\frac{13.25+0.5^{2}+\left(12-8.5\right)^{2}}{7}$$

Calculate 0.5 to the power of 2 and get 0.25.

$$\frac{13.25+0.25+\left(12-8.5\right)^{2}}{7}$$

Add 13.25 and 0.25 to get 13.5.

$$\frac{13.5+\left(12-8.5\right)^{2}}{7}$$

Subtract 8.5 from 12 to get 3.5.

$$\frac{13.5+3.5^{2}}{7}$$

Calculate 3.5 to the power of 2 and get 12.25.

$$\frac{13.5+12.25}{7}$$

Add 13.5 and 12.25 to get 25.75.

$$\frac{25.75}{7}$$

Expand \frac{25.75}{7} by multiplying both numerator and the denominator by 100.

$$\frac{2575}{700}$$

Reduce the fraction \frac{2575}{700} to lowest terms by extracting and canceling out 25.

$$\frac{103}{28}$$

Factor

$$\frac{103}{7 \cdot 2 ^ {2}} = 3\frac{19}{28} = 3.6785714285714284$$