Solve 10*2.5+(1/2)(-9.8)(2.5)^2

$$10 \times 2.5 + ( \frac { 1 } { 2 } ) ( - 9.8 ) ( 2.5 ) ^ { 2 }$$

Evaluate

$$-5.625$$

Solution Steps

Multiply 10 and 2.5 to get 25.

$$25+\frac{1}{2}\left(-9.8\right)\times 2.5^{2}$$

Convert decimal number -9.8 to fraction -\frac{98}{10}. Reduce the fraction -\frac{98}{10} to lowest terms by extracting and canceling out 2.

$$25+\frac{1}{2}\left(-\frac{49}{5}\right)\times 2.5^{2}$$

Multiply \frac{1}{2} times -\frac{49}{5} by multiplying numerator times numerator and denominator times denominator.

$$25+\frac{1\left(-49\right)}{2\times 5}\times 2.5^{2}$$

Do the multiplications in the fraction \frac{1\left(-49\right)}{2\times 5}.

$$25+\frac{-49}{10}\times 2.5^{2}$$

Fraction \frac{-49}{10} can be rewritten as -\frac{49}{10} by extracting the negative sign.

$$25-\frac{49}{10}\times 2.5^{2}$$

Calculate 2.5 to the power of 2 and get 6.25.

$$25-\frac{49}{10}\times 6.25$$

Convert decimal number 6.25 to fraction \frac{625}{100}. Reduce the fraction \frac{625}{100} to lowest terms by extracting and canceling out 25.

$$25-\frac{49}{10}\times \frac{25}{4}$$

Multiply -\frac{49}{10} times \frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$25+\frac{-49\times 25}{10\times 4}$$

Do the multiplications in the fraction \frac{-49\times 25}{10\times 4}.

$$25+\frac{-1225}{40}$$

Reduce the fraction \frac{-1225}{40} to lowest terms by extracting and canceling out 5.

$$25-\frac{245}{8}$$

Convert 25 to fraction \frac{200}{8}.

$$\frac{200}{8}-\frac{245}{8}$$

Since \frac{200}{8} and \frac{245}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{200-245}{8}$$

Subtract 245 from 200 to get -45.

$$-\frac{45}{8}$$

Factor

$$-5.625$$