Solve {left(-1/2-3right)}^2-(-1/2)(5*(-1/2)-6)

$${ \left(- \frac{ 1 }{ 2 } -3 \right) }^{ 2 } -(- \frac{ 1 }{ 2 } )(5 \times (- \frac{ 1 }{ 2 } )-6)$$

Evaluate

$$8$$

Solution Steps

Subtract 3 from -\frac{1}{2} to get -\frac{7}{2}.

$$\left(-\frac{7}{2}\right)^{2}-\left(-\frac{1}{2}\left(5\left(-\frac{1}{2}\right)-6\right)\right)$$

Calculate -\frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$\frac{49}{4}-\left(-\frac{1}{2}\left(5\left(-\frac{1}{2}\right)-6\right)\right)$$

Multiply 5 and -\frac{1}{2} to get -\frac{5}{2}.

$$\frac{49}{4}-\left(-\frac{1}{2}\left(-\frac{5}{2}-6\right)\right)$$

Subtract 6 from -\frac{5}{2} to get -\frac{17}{2}.

$$\frac{49}{4}-\left(-\frac{1}{2}\left(-\frac{17}{2}\right)\right)$$

Multiply -\frac{1}{2} and -\frac{17}{2} to get \frac{17}{4}.

$$\frac{49}{4}-\frac{17}{4}$$

Subtract \frac{17}{4} from \frac{49}{4} to get 8.

$$8$$

Factor

$$2^{3}$$