Solve 65*4.2^2/2-65*4.6^2/2

$$\frac{ 65 \times { 4.2 }^{ 2 } }{ 2 } - \frac{ 65 \times { 4.6 }^{ 2 } }{ 2 }$$

Evaluate

$$-114.4$$

Solution Steps

Calculate 4.2 to the power of 2 and get 17.64.

$$\frac{65\times 17.64}{2}-\frac{65\times 4.6^{2}}{2}$$

Multiply 65 and 17.64 to get 1146.6.

$$\frac{1146.6}{2}-\frac{65\times 4.6^{2}}{2}$$

Expand \frac{1146.6}{2} by multiplying both numerator and the denominator by 10.

$$\frac{11466}{20}-\frac{65\times 4.6^{2}}{2}$$

Reduce the fraction \frac{11466}{20} to lowest terms by extracting and canceling out 2.

$$\frac{5733}{10}-\frac{65\times 4.6^{2}}{2}$$

Calculate 4.6 to the power of 2 and get 21.16.

$$\frac{5733}{10}-\frac{65\times 21.16}{2}$$

Multiply 65 and 21.16 to get 1375.4.

$$\frac{5733}{10}-\frac{1375.4}{2}$$

Expand \frac{1375.4}{2} by multiplying both numerator and the denominator by 10.

$$\frac{5733}{10}-\frac{13754}{20}$$

Reduce the fraction \frac{13754}{20} to lowest terms by extracting and canceling out 2.

$$\frac{5733}{10}-\frac{6877}{10}$$

Since \frac{5733}{10} and \frac{6877}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5733-6877}{10}$$

Subtract 6877 from 5733 to get -1144.

$$\frac{-1144}{10}$$

Reduce the fraction \frac{-1144}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{572}{5}$$

Factor

$$-114.4$$