Solve 2(5/4)^2+5(-5/4)-1

$$2 ( \frac { 5 } { 4 } ) ^ { 2 } + 5 ( - \frac { 5 } { 4 } ) - 1$$

Evaluate

$$-\frac{33}{8}=-4.125$$

Solution Steps

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$2\times \frac{25}{16}+5\left(-\frac{5}{4}\right)-1$$

Express 2\times \frac{25}{16} as a single fraction.

$$\frac{2\times 25}{16}+5\left(-\frac{5}{4}\right)-1$$

Multiply 2 and 25 to get 50.

$$\frac{50}{16}+5\left(-\frac{5}{4}\right)-1$$

Reduce the fraction \frac{50}{16} to lowest terms by extracting and canceling out 2.

$$\frac{25}{8}+5\left(-\frac{5}{4}\right)-1$$

Express 5\left(-\frac{5}{4}\right) as a single fraction.

$$\frac{25}{8}+\frac{5\left(-5\right)}{4}-1$$

Multiply 5 and -5 to get -25.

$$\frac{25}{8}+\frac{-25}{4}-1$$

Fraction \frac{-25}{4} can be rewritten as -\frac{25}{4} by extracting the negative sign.

$$\frac{25}{8}-\frac{25}{4}-1$$

Least common multiple of 8 and 4 is 8. Convert \frac{25}{8} and \frac{25}{4} to fractions with denominator 8.

$$\frac{25}{8}-\frac{50}{8}-1$$

Since \frac{25}{8} and \frac{50}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-50}{8}-1$$

Subtract 50 from 25 to get -25.

$$-\frac{25}{8}-1$$

Convert 1 to fraction \frac{8}{8}.

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

Since -\frac{25}{8} and \frac{8}{8} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 8 from -25 to get -33.

$$-\frac{33}{8}$$

Factor

$$-\frac{33}{8} = -4\frac{1}{8} = -4.125$$