Solve -1/6(-2)^3+1/2(-2)^2+4(-2)

$$- \frac { 1 } { 6 } ( - 2 ) ^ { 3 } + \frac { 1 } { 2 } ( - 2 ) ^ { 2 } + 4 ( - 2 )$$

Evaluate

$$-\frac{14}{3}\approx -4.666666667$$

Solution Steps

Calculate -2 to the power of 3 and get -8.

$$-\frac{1}{6}\left(-8\right)+\frac{1}{2}\left(-2\right)^{2}+4\left(-2\right)$$

Express -\frac{1}{6}\left(-8\right) as a single fraction.

$$\frac{-\left(-8\right)}{6}+\frac{1}{2}\left(-2\right)^{2}+4\left(-2\right)$$

Multiply -1 and -8 to get 8.

$$\frac{8}{6}+\frac{1}{2}\left(-2\right)^{2}+4\left(-2\right)$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

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

Calculate -2 to the power of 2 and get 4.

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

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

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

Divide 4 by 2 to get 2.

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

Convert 2 to fraction \frac{6}{3}.

$$\frac{4}{3}+\frac{6}{3}+4\left(-2\right)$$

Since \frac{4}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

$$\frac{4+6}{3}+4\left(-2\right)$$

Add 4 and 6 to get 10.

$$\frac{10}{3}+4\left(-2\right)$$

Multiply 4 and -2 to get -8.

$$\frac{10}{3}-8$$

Convert 8 to fraction \frac{24}{3}.

$$\frac{10}{3}-\frac{24}{3}$$

Since \frac{10}{3} and \frac{24}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-24}{3}$$

Subtract 24 from 10 to get -14.

$$-\frac{14}{3}$$

Factor

$$-\frac{14}{3} = -4\frac{2}{3} = -4.666666666666667$$