Solve 5left(11.8-7.73right)^2+5left(3.8-7.73right)^2+5left(76-7.73right)^2/3-1

$$\frac{ 5 { \left(11.8-7.73 \right) }^{ 2 } +5 { \left(3.8-7.73 \right) }^{ 2 } +5 { \left(76-7.73 \right) }^{ 2 } }{ 3-1 }$$

Evaluate

$$11732.00675$$

Solution Steps

Subtract 7.73 from 11.8 to get 4.07.

$$\frac{5\times 4.07^{2}+5\left(3.8-7.73\right)^{2}+5\left(76-7.73\right)^{2}}{3-1}$$

Calculate 4.07 to the power of 2 and get 16.5649.

$$\frac{5\times 16.5649+5\left(3.8-7.73\right)^{2}+5\left(76-7.73\right)^{2}}{3-1}$$

Multiply 5 and 16.5649 to get 82.8245.

$$\frac{82.8245+5\left(3.8-7.73\right)^{2}+5\left(76-7.73\right)^{2}}{3-1}$$

Subtract 7.73 from 3.8 to get -3.93.

$$\frac{82.8245+5\left(-3.93\right)^{2}+5\left(76-7.73\right)^{2}}{3-1}$$

Calculate -3.93 to the power of 2 and get 15.4449.

$$\frac{82.8245+5\times 15.4449+5\left(76-7.73\right)^{2}}{3-1}$$

Multiply 5 and 15.4449 to get 77.2245.

$$\frac{82.8245+77.2245+5\left(76-7.73\right)^{2}}{3-1}$$

Add 82.8245 and 77.2245 to get 160.049.

$$\frac{160.049+5\left(76-7.73\right)^{2}}{3-1}$$

Subtract 7.73 from 76 to get 68.27.

$$\frac{160.049+5\times 68.27^{2}}{3-1}$$

Calculate 68.27 to the power of 2 and get 4660.7929.

$$\frac{160.049+5\times 4660.7929}{3-1}$$

Multiply 5 and 4660.7929 to get 23303.9645.

$$\frac{160.049+23303.9645}{3-1}$$

Add 160.049 and 23303.9645 to get 23464.0135.

$$\frac{23464.0135}{3-1}$$

Subtract 1 from 3 to get 2.

$$\frac{23464.0135}{2}$$

Expand \frac{23464.0135}{2} by multiplying both numerator and the denominator by 10000.

$$\frac{234640135}{20000}$$

Reduce the fraction \frac{234640135}{20000} to lowest terms by extracting and canceling out 5.

$$\frac{46928027}{4000}$$

Factor

$$\frac{23 \cdot 1031 \cdot 1979}{2 ^ {5} \cdot 5 ^ {3}} = 11732\frac{27}{4000} = 11732.00675$$