Solve (n-11)+1/2(n+1)(n-12)

$$( n - 11 ) + \frac { 1 } { 2 } ( n + 1 ) ( n - 12 )$$

Evaluate

$$\frac{n^{2}-9n-34}{2}$$

Solution Steps

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

$$n-11+\left(\frac{1}{2}n+\frac{1}{2}\right)\left(n-12\right)$$

Apply the distributive property by multiplying each term of \frac{1}{2}n+\frac{1}{2} by each term of n-12.

$$n-11+\frac{1}{2}nn+\frac{1}{2}n\left(-12\right)+\frac{1}{2}n+\frac{1}{2}\left(-12\right)$$

Multiply n and n to get n^{2}.

$$n-11+\frac{1}{2}n^{2}+\frac{1}{2}n\left(-12\right)+\frac{1}{2}n+\frac{1}{2}\left(-12\right)$$

Multiply \frac{1}{2} and -12 to get \frac{-12}{2}.

$$n-11+\frac{1}{2}n^{2}+\frac{-12}{2}n+\frac{1}{2}n+\frac{1}{2}\left(-12\right)$$

Divide -12 by 2 to get -6.

$$n-11+\frac{1}{2}n^{2}-6n+\frac{1}{2}n+\frac{1}{2}\left(-12\right)$$

Combine -6n and \frac{1}{2}n to get -\frac{11}{2}n.

$$n-11+\frac{1}{2}n^{2}-\frac{11}{2}n+\frac{1}{2}\left(-12\right)$$

Multiply \frac{1}{2} and -12 to get \frac{-12}{2}.

$$n-11+\frac{1}{2}n^{2}-\frac{11}{2}n+\frac{-12}{2}$$

Divide -12 by 2 to get -6.

$$n-11+\frac{1}{2}n^{2}-\frac{11}{2}n-6$$

Combine n and -\frac{11}{2}n to get -\frac{9}{2}n.

$$-\frac{9}{2}n-11+\frac{1}{2}n^{2}-6$$

Subtract 6 from -11 to get -17.

$$-\frac{9}{2}n-17+\frac{1}{2}n^{2}$$

Expand

$$\frac{n^{2}}{2}-\frac{9n}{2}-17$$

Solution Steps

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

$$n-11+\left(\frac{1}{2}n+\frac{1}{2}\right)\left(n-12\right)$$

Apply the distributive property by multiplying each term of \frac{1}{2}n+\frac{1}{2} by each term of n-12.

$$n-11+\frac{1}{2}nn+\frac{1}{2}n\left(-12\right)+\frac{1}{2}n+\frac{1}{2}\left(-12\right)$$

Multiply n and n to get n^{2}.

$$n-11+\frac{1}{2}n^{2}+\frac{1}{2}n\left(-12\right)+\frac{1}{2}n+\frac{1}{2}\left(-12\right)$$

Multiply \frac{1}{2} and -12 to get \frac{-12}{2}.

$$n-11+\frac{1}{2}n^{2}+\frac{-12}{2}n+\frac{1}{2}n+\frac{1}{2}\left(-12\right)$$

Divide -12 by 2 to get -6.

$$n-11+\frac{1}{2}n^{2}-6n+\frac{1}{2}n+\frac{1}{2}\left(-12\right)$$

Combine -6n and \frac{1}{2}n to get -\frac{11}{2}n.

$$n-11+\frac{1}{2}n^{2}-\frac{11}{2}n+\frac{1}{2}\left(-12\right)$$

Multiply \frac{1}{2} and -12 to get \frac{-12}{2}.

$$n-11+\frac{1}{2}n^{2}-\frac{11}{2}n+\frac{-12}{2}$$

Divide -12 by 2 to get -6.

$$n-11+\frac{1}{2}n^{2}-\frac{11}{2}n-6$$

Combine n and -\frac{11}{2}n to get -\frac{9}{2}n.

$$-\frac{9}{2}n-11+\frac{1}{2}n^{2}-6$$

Subtract 6 from -11 to get -17.

$$-\frac{9}{2}n-17+\frac{1}{2}n^{2}$$