Solve left(85-84.625right)^2+left(85-84.625right)^2+left(87-84.625right)^2+left(81-84.625right)^2+{left(80-84.625right)}^2+{left(79-84.625right)}^2+{left(87-84.625right)}^2+{left(93-84.625right)}^2

$${ \left(85-84.625 \right) }^{ 2 } + { \left(85-84.625 \right) }^{ 2 } + { \left(87-84.625 \right) }^{ 2 } + { \left(81-84.625 \right) }^{ 2 } + { \left(80-84.625 \right) }^{ 2 } + { \left(79-84.625 \right) }^{ 2 } + { \left(87-84.625 \right) }^{ 2 } + { \left(93-84.625 \right) }^{ 2 }$$

Evaluate

$$147.875$$

Solution Steps

Subtract 84.625 from 85 to get 0.375.

$$0.375^{2}+\left(85-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(81-84.625\right)^{2}+\left(80-84.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Calculate 0.375 to the power of 2 and get 0.140625.

$$0.140625+\left(85-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(81-84.625\right)^{2}+\left(80-84.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Subtract 84.625 from 85 to get 0.375.

$$0.140625+0.375^{2}+\left(87-84.625\right)^{2}+\left(81-84.625\right)^{2}+\left(80-84.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Calculate 0.375 to the power of 2 and get 0.140625.

$$0.140625+0.140625+\left(87-84.625\right)^{2}+\left(81-84.625\right)^{2}+\left(80-84.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Add 0.140625 and 0.140625 to get 0.28125.

$$0.28125+\left(87-84.625\right)^{2}+\left(81-84.625\right)^{2}+\left(80-84.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Subtract 84.625 from 87 to get 2.375.

$$0.28125+2.375^{2}+\left(81-84.625\right)^{2}+\left(80-84.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Calculate 2.375 to the power of 2 and get 5.640625.

$$0.28125+5.640625+\left(81-84.625\right)^{2}+\left(80-84.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Add 0.28125 and 5.640625 to get 5.921875.

$$5.921875+\left(81-84.625\right)^{2}+\left(80-84.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Subtract 84.625 from 81 to get -3.625.

$$5.921875+\left(-3.625\right)^{2}+\left(80-84.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Calculate -3.625 to the power of 2 and get 13.140625.

$$5.921875+13.140625+\left(80-84.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Add 5.921875 and 13.140625 to get 19.0625.

$$19.0625+\left(80-84.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Subtract 84.625 from 80 to get -4.625.

$$19.0625+\left(-4.625\right)^{2}+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Calculate -4.625 to the power of 2 and get 21.390625.

$$19.0625+21.390625+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Add 19.0625 and 21.390625 to get 40.453125.

$$40.453125+\left(79-84.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Subtract 84.625 from 79 to get -5.625.

$$40.453125+\left(-5.625\right)^{2}+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Calculate -5.625 to the power of 2 and get 31.640625.

$$40.453125+31.640625+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Add 40.453125 and 31.640625 to get 72.09375.

$$72.09375+\left(87-84.625\right)^{2}+\left(93-84.625\right)^{2}$$

Subtract 84.625 from 87 to get 2.375.

$$72.09375+2.375^{2}+\left(93-84.625\right)^{2}$$

Calculate 2.375 to the power of 2 and get 5.640625.

$$72.09375+5.640625+\left(93-84.625\right)^{2}$$

Add 72.09375 and 5.640625 to get 77.734375.

$$77.734375+\left(93-84.625\right)^{2}$$

Subtract 84.625 from 93 to get 8.375.

$$77.734375+8.375^{2}$$

Calculate 8.375 to the power of 2 and get 70.140625.

$$77.734375+70.140625$$

Add 77.734375 and 70.140625 to get 147.875.

$$147.875$$

Factor

$$\frac{7 \cdot 13 ^ {2}}{2 ^ {3}} = 147\frac{7}{8} = 147.875$$