Solve 46.6^2/10+25.1^2/10+23.9^2/10+20^2/10-334.084

$$\frac{ { 46.6 }^{ 2 } }{ 10 } + \frac{ { 25.1 }^{ 2 } }{ 10 } + \frac{ { 23.9 }^{ 2 } }{ 10 } + \frac{ { 20 }^{ 2 } }{ 10 } -334.084$$

Evaluate

$$43.194$$

Solution Steps

Calculate 46.6 to the power of 2 and get 2171.56.

$$\frac{2171.56}{10}+\frac{25.1^{2}}{10}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084$$

Expand \frac{2171.56}{10} by multiplying both numerator and the denominator by 100.

$$\frac{217156}{1000}+\frac{25.1^{2}}{10}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084$$

Reduce the fraction \frac{217156}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{54289}{250}+\frac{25.1^{2}}{10}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084$$

Calculate 25.1 to the power of 2 and get 630.01.

$$\frac{54289}{250}+\frac{630.01}{10}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084$$

Expand \frac{630.01}{10} by multiplying both numerator and the denominator by 100.

$$\frac{54289}{250}+\frac{63001}{1000}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084$$

Least common multiple of 250 and 1000 is 1000. Convert \frac{54289}{250} and \frac{63001}{1000} to fractions with denominator 1000.

$$\frac{217156}{1000}+\frac{63001}{1000}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084$$

Since \frac{217156}{1000} and \frac{63001}{1000} have the same denominator, add them by adding their numerators.

$$\frac{217156+63001}{1000}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084$$

Add 217156 and 63001 to get 280157.

$$\frac{280157}{1000}+\frac{23.9^{2}}{10}+\frac{20^{2}}{10}-334.084$$

Calculate 23.9 to the power of 2 and get 571.21.

$$\frac{280157}{1000}+\frac{571.21}{10}+\frac{20^{2}}{10}-334.084$$

Expand \frac{571.21}{10} by multiplying both numerator and the denominator by 100.

$$\frac{280157}{1000}+\frac{57121}{1000}+\frac{20^{2}}{10}-334.084$$

Since \frac{280157}{1000} and \frac{57121}{1000} have the same denominator, add them by adding their numerators.

$$\frac{280157+57121}{1000}+\frac{20^{2}}{10}-334.084$$

Add 280157 and 57121 to get 337278.

$$\frac{337278}{1000}+\frac{20^{2}}{10}-334.084$$

Reduce the fraction \frac{337278}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{168639}{500}+\frac{20^{2}}{10}-334.084$$

Calculate 20 to the power of 2 and get 400.

$$\frac{168639}{500}+\frac{400}{10}-334.084$$

Divide 400 by 10 to get 40.

$$\frac{168639}{500}+40-334.084$$

Convert 40 to fraction \frac{20000}{500}.

$$\frac{168639}{500}+\frac{20000}{500}-334.084$$

Since \frac{168639}{500} and \frac{20000}{500} have the same denominator, add them by adding their numerators.

$$\frac{168639+20000}{500}-334.084$$

Add 168639 and 20000 to get 188639.

$$\frac{188639}{500}-334.084$$

Convert decimal number 334.084 to fraction \frac{334084}{1000}. Reduce the fraction \frac{334084}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{188639}{500}-\frac{83521}{250}$$

Least common multiple of 500 and 250 is 500. Convert \frac{188639}{500} and \frac{83521}{250} to fractions with denominator 500.

$$\frac{188639}{500}-\frac{167042}{500}$$

Since \frac{188639}{500} and \frac{167042}{500} have the same denominator, subtract them by subtracting their numerators.

$$\frac{188639-167042}{500}$$

Subtract 167042 from 188639 to get 21597.

$$\frac{21597}{500}$$

Factor

$$\frac{3 \cdot 23 \cdot 313}{2 ^ {2} \cdot 5 ^ {3}} = 43\frac{97}{500} = 43.194$$