Solve left(10.1-10right)^2*2+left(9.99-10right)^2*2+left(9.98-10right)^2*2+left(9.94-10right)^2+{left(10.03-10right)}^2*2+{left(9.95-10right)}^2

$${ \left(10.1-10 \right) }^{ 2 } \times 2+ { \left(9.99-10 \right) }^{ 2 } \times 2+ { \left(9.98-10 \right) }^{ 2 } \times 2+ { \left(9.94-10 \right) }^{ 2 } + { \left(10.03-10 \right) }^{ 2 } \times 2+ { \left(9.95-10 \right) }^{ 2 }$$

Evaluate

$$0.0289$$

Solution Steps

Subtract 10 from 10.1 to get 0.1.

$$0.1^{2}\times 2+\left(9.99-10\right)^{2}\times 2+\left(9.98-10\right)^{2}\times 2+\left(9.94-10\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Calculate 0.1 to the power of 2 and get 0.01.

$$0.01\times 2+\left(9.99-10\right)^{2}\times 2+\left(9.98-10\right)^{2}\times 2+\left(9.94-10\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Multiply 0.01 and 2 to get 0.02.

$$0.02+\left(9.99-10\right)^{2}\times 2+\left(9.98-10\right)^{2}\times 2+\left(9.94-10\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Subtract 10 from 9.99 to get -0.01.

$$0.02+\left(-0.01\right)^{2}\times 2+\left(9.98-10\right)^{2}\times 2+\left(9.94-10\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Calculate -0.01 to the power of 2 and get 0.0001.

$$0.02+0.0001\times 2+\left(9.98-10\right)^{2}\times 2+\left(9.94-10\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Multiply 0.0001 and 2 to get 0.0002.

$$0.02+0.0002+\left(9.98-10\right)^{2}\times 2+\left(9.94-10\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Add 0.02 and 0.0002 to get 0.0202.

$$0.0202+\left(9.98-10\right)^{2}\times 2+\left(9.94-10\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Subtract 10 from 9.98 to get -0.02.

$$0.0202+\left(-0.02\right)^{2}\times 2+\left(9.94-10\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Calculate -0.02 to the power of 2 and get 0.0004.

$$0.0202+0.0004\times 2+\left(9.94-10\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Multiply 0.0004 and 2 to get 0.0008.

$$0.0202+0.0008+\left(9.94-10\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Add 0.0202 and 0.0008 to get 0.021.

$$0.021+\left(9.94-10\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Subtract 10 from 9.94 to get -0.06.

$$0.021+\left(-0.06\right)^{2}+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Calculate -0.06 to the power of 2 and get 0.0036.

$$0.021+0.0036+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Add 0.021 and 0.0036 to get 0.0246.

$$0.0246+\left(10.03-10\right)^{2}\times 2+\left(9.95-10\right)^{2}$$

Subtract 10 from 10.03 to get 0.03.

$$0.0246+0.03^{2}\times 2+\left(9.95-10\right)^{2}$$

Calculate 0.03 to the power of 2 and get 0.0009.

$$0.0246+0.0009\times 2+\left(9.95-10\right)^{2}$$

Multiply 0.0009 and 2 to get 0.0018.

$$0.0246+0.0018+\left(9.95-10\right)^{2}$$

Add 0.0246 and 0.0018 to get 0.0264.

$$0.0264+\left(9.95-10\right)^{2}$$

Subtract 10 from 9.95 to get -0.05.

$$0.0264+\left(-0.05\right)^{2}$$

Calculate -0.05 to the power of 2 and get 0.0025.

$$0.0264+0.0025$$

Add 0.0264 and 0.0025 to get 0.0289.

$$0.0289$$

Factor

$$\frac{17 ^ {2}}{2 ^ {4} \cdot 5 ^ {4}} = 0.0289$$