Solve (-1/2)^3-4(-1/2)^2+12(-1/2)+7

$$( - \frac { 1 } { 2 } ) ^ { 3 } - 4 ( - \frac { 1 } { 2 } ) ^ { 2 } + 12 ( - \frac { 1 } { 2 } ) + 7$$

Evaluate

$$-\frac{1}{8}=-0.125$$

Solution Steps

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$-\frac{1}{8}-4\left(-\frac{1}{2}\right)^{2}+12\left(-\frac{1}{2}\right)+7$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-\frac{1}{8}-4\times \frac{1}{4}+12\left(-\frac{1}{2}\right)+7$$

Cancel out 4 and 4.

$$-\frac{1}{8}-1+12\left(-\frac{1}{2}\right)+7$$

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

$$-\frac{1}{8}-\frac{8}{8}+12\left(-\frac{1}{2}\right)+7$$

Since -\frac{1}{8} and \frac{8}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-8}{8}+12\left(-\frac{1}{2}\right)+7$$

Subtract 8 from -1 to get -9.

$$-\frac{9}{8}+12\left(-\frac{1}{2}\right)+7$$

Express 12\left(-\frac{1}{2}\right) as a single fraction.

$$-\frac{9}{8}+\frac{12\left(-1\right)}{2}+7$$

Multiply 12 and -1 to get -12.

$$-\frac{9}{8}+\frac{-12}{2}+7$$

Divide -12 by 2 to get -6.

$$-\frac{9}{8}-6+7$$

Convert 6 to fraction \frac{48}{8}.

$$-\frac{9}{8}-\frac{48}{8}+7$$

Since -\frac{9}{8} and \frac{48}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-48}{8}+7$$

Subtract 48 from -9 to get -57.

$$-\frac{57}{8}+7$$

Convert 7 to fraction \frac{56}{8}.

$$-\frac{57}{8}+\frac{56}{8}$$

Since -\frac{57}{8} and \frac{56}{8} have the same denominator, add them by adding their numerators.

$$\frac{-57+56}{8}$$

Add -57 and 56 to get -1.

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

Factor

$$-\frac{1}{8} = -0.125$$