Solve left(1.009-1.0175right)^2+left(1.009-1.0087right)^2+left(1.009-1.0073right)^2+left(1.009-1.0013right)^2+{left(1.009-1.0194right)}^{2}+{left(1.009-1.0064right)}^{2}+{left(1.009-0.9975right)}^2+{left(1.009-1.0071right)}^2+{left(1.009-1.0193right)}^2+{left(1.009-1.0057right)}^2

$${ \left(1.009-1.0175 \right) }^{ 2 } + { \left(1.009-1.0087 \right) }^{ 2 } + { \left(1.009-1.0073 \right) }^{ 2 } + { \left(1.009-1.0013 \right) }^{ 2 } + { \left(1.009-1.0194 \right) }^{ 2 } + { \left(1.009-1.0064 \right) }^{ 2 } + { \left(1.009-0.9975 \right) }^{ 2 } + { \left(1.009-1.0071 \right) }^{ 2 } + { \left(1.009-1.0193 \right) }^{ 2 } + { \left(1.009-1.0057 \right) }^{ 2 }$$

Evaluate

$$0.00050228$$

Solution Steps

Subtract 1.0175 from 1.009 to get -0.0085.

$$\left(-0.0085\right)^{2}+\left(1.009-1.0087\right)^{2}+\left(1.009-1.0073\right)^{2}+\left(1.009-1.0013\right)^{2}+\left(1.009-1.0194\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Calculate -0.0085 to the power of 2 and get 0.00007225.

$$0.00007225+\left(1.009-1.0087\right)^{2}+\left(1.009-1.0073\right)^{2}+\left(1.009-1.0013\right)^{2}+\left(1.009-1.0194\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Subtract 1.0087 from 1.009 to get 0.0003.

$$0.00007225+0.0003^{2}+\left(1.009-1.0073\right)^{2}+\left(1.009-1.0013\right)^{2}+\left(1.009-1.0194\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Calculate 0.0003 to the power of 2 and get 0.00000009.

$$0.00007225+0.00000009+\left(1.009-1.0073\right)^{2}+\left(1.009-1.0013\right)^{2}+\left(1.009-1.0194\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Add 0.00007225 and 0.00000009 to get 0.00007234.

$$0.00007234+\left(1.009-1.0073\right)^{2}+\left(1.009-1.0013\right)^{2}+\left(1.009-1.0194\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Subtract 1.0073 from 1.009 to get 0.0017.

$$0.00007234+0.0017^{2}+\left(1.009-1.0013\right)^{2}+\left(1.009-1.0194\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Calculate 0.0017 to the power of 2 and get 0.00000289.

$$0.00007234+0.00000289+\left(1.009-1.0013\right)^{2}+\left(1.009-1.0194\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Add 0.00007234 and 0.00000289 to get 0.00007523.

$$0.00007523+\left(1.009-1.0013\right)^{2}+\left(1.009-1.0194\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Subtract 1.0013 from 1.009 to get 0.0077.

$$0.00007523+0.0077^{2}+\left(1.009-1.0194\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Calculate 0.0077 to the power of 2 and get 0.00005929.

$$0.00007523+0.00005929+\left(1.009-1.0194\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Add 0.00007523 and 0.00005929 to get 0.00013452.

$$0.00013452+\left(1.009-1.0194\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Subtract 1.0194 from 1.009 to get -0.0104.

$$0.00013452+\left(-0.0104\right)^{2}+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Calculate -0.0104 to the power of 2 and get 0.00010816.

$$0.00013452+0.00010816+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Add 0.00013452 and 0.00010816 to get 0.00024268.

$$0.00024268+\left(1.009-1.0064\right)^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Subtract 1.0064 from 1.009 to get 0.0026.

$$0.00024268+0.0026^{2}+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Calculate 0.0026 to the power of 2 and get 0.00000676.

$$0.00024268+0.00000676+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Add 0.00024268 and 0.00000676 to get 0.00024944.

$$0.00024944+\left(1.009-0.9975\right)^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Subtract 0.9975 from 1.009 to get 0.0115.

$$0.00024944+0.0115^{2}+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Calculate 0.0115 to the power of 2 and get 0.00013225.

$$0.00024944+0.00013225+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Add 0.00024944 and 0.00013225 to get 0.00038169.

$$0.00038169+\left(1.009-1.0071\right)^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Subtract 1.0071 from 1.009 to get 0.0019.

$$0.00038169+0.0019^{2}+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Calculate 0.0019 to the power of 2 and get 0.00000361.

$$0.00038169+0.00000361+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Add 0.00038169 and 0.00000361 to get 0.0003853.

$$0.0003853+\left(1.009-1.0193\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Subtract 1.0193 from 1.009 to get -0.0103.

$$0.0003853+\left(-0.0103\right)^{2}+\left(1.009-1.0057\right)^{2}$$

Calculate -0.0103 to the power of 2 and get 0.00010609.

$$0.0003853+0.00010609+\left(1.009-1.0057\right)^{2}$$

Add 0.0003853 and 0.00010609 to get 0.00049139.

$$0.00049139+\left(1.009-1.0057\right)^{2}$$

Subtract 1.0057 from 1.009 to get 0.0033.

$$0.00049139+0.0033^{2}$$

Calculate 0.0033 to the power of 2 and get 0.00001089.

$$0.00049139+0.00001089$$

Add 0.00049139 and 0.00001089 to get 0.00050228.

$$0.00050228$$

Factor

$$\frac{29 \cdot 433}{2 ^ {6} \cdot 5 ^ {8}} = 0.00050228$$