Solve 4(-1/2)^2-(p+1)(-1/2)-12

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

Evaluate

$$\frac{p-21}{2}$$

Solution Steps

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

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

Cancel out 4 and 4.

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

Use the distributive property to multiply p+1 by -\frac{1}{2}.

$$1-\left(p\left(-\frac{1}{2}\right)-\frac{1}{2}\right)-12$$

To find the opposite of p\left(-\frac{1}{2}\right)-\frac{1}{2}, find the opposite of each term.

$$1-p\left(-\frac{1}{2}\right)-\left(-\frac{1}{2}\right)-12$$

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

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

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$1+\frac{1}{2}p+\frac{1}{2}-12$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{2}{2}+\frac{1}{2}p+\frac{1}{2}-12$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{2}+\frac{1}{2}p-12$$

Add 2 and 1 to get 3.

$$\frac{3}{2}+\frac{1}{2}p-12$$

Convert 12 to fraction \frac{24}{2}.

$$\frac{3}{2}+\frac{1}{2}p-\frac{24}{2}$$

Since \frac{3}{2} and \frac{24}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-24}{2}+\frac{1}{2}p$$

Subtract 24 from 3 to get -21.

$$-\frac{21}{2}+\frac{1}{2}p$$

Expand

$$\frac{p-21}{2}$$

Solution Steps

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

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

Cancel out 4 and 4.

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

Use the distributive property to multiply p+1 by -\frac{1}{2}.

$$1-\left(p\left(-\frac{1}{2}\right)-\frac{1}{2}\right)-12$$

To find the opposite of p\left(-\frac{1}{2}\right)-\frac{1}{2}, find the opposite of each term.

$$1-p\left(-\frac{1}{2}\right)-\left(-\frac{1}{2}\right)-12$$

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

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

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$1+\frac{1}{2}p+\frac{1}{2}-12$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{2}{2}+\frac{1}{2}p+\frac{1}{2}-12$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{2}+\frac{1}{2}p-12$$

Add 2 and 1 to get 3.

$$\frac{3}{2}+\frac{1}{2}p-12$$

Convert 12 to fraction \frac{24}{2}.

$$\frac{3}{2}+\frac{1}{2}p-\frac{24}{2}$$

Since \frac{3}{2} and \frac{24}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-24}{2}+\frac{1}{2}p$$

Subtract 24 from 3 to get -21.

$$-\frac{21}{2}+\frac{1}{2}p$$