Solve {l}{(k-4/2)^2+(2+k/2)^2}{+3k+6}

$$\left. \begin{array} { l } { ( \frac { k - 4 } { 2 } ) ^ { 2 } + ( \frac { 2 + k } { 2 } ) ^ { 2 } } \\ { + 3 k + 6 } \end{array} \right.$$

Evaluate

$$\frac{k^{2}}{2}+2k+11$$

Short Solution Steps

To raise \frac{k-4}{2} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{2+k}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Since \frac{\left(k-4\right)^{2}}{2^{2}} and \frac{\left(2+k\right)^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(k-4\right)^{2}+\left(2+k\right)^{2}.

$$\frac{k^{2}-8k+16+4+4k+k^{2}}{2^{2}}+3k+6$$

Combine like terms in k^{2}-8k+16+4+4k+k^{2}.

$$\frac{2k^{2}-4k+20}{2^{2}}+3k+6$$

Factor the expressions that are not already factored in \frac{2k^{2}-4k+20}{2^{2}}.

$$\frac{2\left(k^{2}-2k+10\right)}{2^{2}}+3k+6$$

Cancel out 2 in both numerator and denominator.

$$\frac{k^{2}-2k+10}{2}+3k+6$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3k+6 times \frac{2}{2}.

$$\frac{k^{2}-2k+10}{2}+\frac{2\left(3k+6\right)}{2}$$

Since \frac{k^{2}-2k+10}{2} and \frac{2\left(3k+6\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{k^{2}-2k+10+2\left(3k+6\right)}{2}$$

Do the multiplications in k^{2}-2k+10+2\left(3k+6\right).

$$\frac{k^{2}-2k+10+6k+12}{2}$$

Combine like terms in k^{2}-2k+10+6k+12.

$$\frac{k^{2}+4k+22}{2}$$

Expand

$$\frac{k^{2}}{2}+2k+11$$

Short Solution Steps

To raise \frac{k-4}{2} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{2+k}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Since \frac{\left(k-4\right)^{2}}{2^{2}} and \frac{\left(2+k\right)^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(k-4\right)^{2}+\left(2+k\right)^{2}.

$$\frac{k^{2}-8k+16+4+4k+k^{2}}{2^{2}}+3k+6$$

Combine like terms in k^{2}-8k+16+4+4k+k^{2}.

$$\frac{2k^{2}-4k+20}{2^{2}}+3k+6$$

Factor the expressions that are not already factored in \frac{2k^{2}-4k+20}{2^{2}}.

$$\frac{2\left(k^{2}-2k+10\right)}{2^{2}}+3k+6$$

Cancel out 2 in both numerator and denominator.

$$\frac{k^{2}-2k+10}{2}+3k+6$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3k+6 times \frac{2}{2}.

$$\frac{k^{2}-2k+10}{2}+\frac{2\left(3k+6\right)}{2}$$

Since \frac{k^{2}-2k+10}{2} and \frac{2\left(3k+6\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{k^{2}-2k+10+2\left(3k+6\right)}{2}$$

Do the multiplications in k^{2}-2k+10+2\left(3k+6\right).

$$\frac{k^{2}-2k+10+6k+12}{2}$$

Combine like terms in k^{2}-2k+10+6k+12.

$$\frac{k^{2}+4k+22}{2}$$