Solve 2(-3/4)^2+3(-3/4)-1

$$2 ( - \frac { 3 } { 4 } ) ^ { 2 } + 3 ( - \frac { 3 } { 4 } ) - 1$$

Evaluate

$$-\frac{17}{8}=-2.125$$

Solution Steps

Calculate -\frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$2\times \frac{9}{16}+3\left(-\frac{3}{4}\right)-1$$

Express 2\times \frac{9}{16} as a single fraction.

$$\frac{2\times 9}{16}+3\left(-\frac{3}{4}\right)-1$$

Multiply 2 and 9 to get 18.

$$\frac{18}{16}+3\left(-\frac{3}{4}\right)-1$$

Reduce the fraction \frac{18}{16} to lowest terms by extracting and canceling out 2.

$$\frac{9}{8}+3\left(-\frac{3}{4}\right)-1$$

Express 3\left(-\frac{3}{4}\right) as a single fraction.

$$\frac{9}{8}+\frac{3\left(-3\right)}{4}-1$$

Multiply 3 and -3 to get -9.

$$\frac{9}{8}+\frac{-9}{4}-1$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$\frac{9}{8}-\frac{9}{4}-1$$

Least common multiple of 8 and 4 is 8. Convert \frac{9}{8} and \frac{9}{4} to fractions with denominator 8.

$$\frac{9}{8}-\frac{18}{8}-1$$

Since \frac{9}{8} and \frac{18}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-18}{8}-1$$

Subtract 18 from 9 to get -9.

$$-\frac{9}{8}-1$$

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

$$-\frac{9}{8}-\frac{8}{8}$$

Since -\frac{9}{8} and \frac{8}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-8}{8}$$

Subtract 8 from -9 to get -17.

$$-\frac{17}{8}$$

Factor

$$-\frac{17}{8} = -2\frac{1}{8} = -2.125$$