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

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

Evaluate

$$-\frac{25}{4}=-6.25$$

Solution Steps

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

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

Express 3\left(-\frac{3}{2}\right) as a single fraction.

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

Multiply 3 and -3 to get -9.

$$\frac{9}{4}+\frac{-9}{2}-4$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$\frac{9}{4}-\frac{9}{2}-4$$

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{9}{2} to fractions with denominator 4.

$$\frac{9}{4}-\frac{18}{4}-4$$

Since \frac{9}{4} and \frac{18}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-18}{4}-4$$

Subtract 18 from 9 to get -9.

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

Convert 4 to fraction \frac{16}{4}.

$$-\frac{9}{4}-\frac{16}{4}$$

Since -\frac{9}{4} and \frac{16}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-16}{4}$$

Subtract 16 from -9 to get -25.

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

Factor

$$-\frac{25}{4} = -6\frac{1}{4} = -6.25$$