Solve 20left(38.65-33.8right)^2+20left(22.15-33.8right)^2+20left(40.6-33.8right)^2/3-1

$$\frac{ 20 { \left(38.65-33.8 \right) }^{ 2 } +20 { \left(22.15-33.8 \right) }^{ 2 } +20 { \left(40.6-33.8 \right) }^{ 2 } }{ 3-1 }$$

Evaluate

$$2054.85$$

Solution Steps

Subtract 33.8 from 38.65 to get 4.85.

$$\frac{20\times 4.85^{2}+20\left(22.15-33.8\right)^{2}+20\left(40.6-33.8\right)^{2}}{3-1}$$

Calculate 4.85 to the power of 2 and get 23.5225.

$$\frac{20\times 23.5225+20\left(22.15-33.8\right)^{2}+20\left(40.6-33.8\right)^{2}}{3-1}$$

Multiply 20 and 23.5225 to get 470.45.

$$\frac{470.45+20\left(22.15-33.8\right)^{2}+20\left(40.6-33.8\right)^{2}}{3-1}$$

Subtract 33.8 from 22.15 to get -11.65.

$$\frac{470.45+20\left(-11.65\right)^{2}+20\left(40.6-33.8\right)^{2}}{3-1}$$

Calculate -11.65 to the power of 2 and get 135.7225.

$$\frac{470.45+20\times 135.7225+20\left(40.6-33.8\right)^{2}}{3-1}$$

Multiply 20 and 135.7225 to get 2714.45.

$$\frac{470.45+2714.45+20\left(40.6-33.8\right)^{2}}{3-1}$$

Add 470.45 and 2714.45 to get 3184.9.

$$\frac{3184.9+20\left(40.6-33.8\right)^{2}}{3-1}$$

Subtract 33.8 from 40.6 to get 6.8.

$$\frac{3184.9+20\times 6.8^{2}}{3-1}$$

Calculate 6.8 to the power of 2 and get 46.24.

$$\frac{3184.9+20\times 46.24}{3-1}$$

Multiply 20 and 46.24 to get 924.8.

$$\frac{3184.9+924.8}{3-1}$$

Add 3184.9 and 924.8 to get 4109.7.

$$\frac{4109.7}{3-1}$$

Subtract 1 from 3 to get 2.

$$\frac{4109.7}{2}$$

Expand \frac{4109.7}{2} by multiplying both numerator and the denominator by 10.

$$\frac{41097}{20}$$

Factor

$$\frac{3 \cdot 7 \cdot 19 \cdot 103}{5 \cdot 2 ^ {2}} = 2054\frac{17}{20} = 2054.85$$