$$N(x)= \frac{ 1 }{ 2 } { \left(x+3 \right) }^{ 2 }$$
$\frac{\left(x+3\right)^{2}}{2}$
$$\frac{1}{2}\left(x^{2}+6x+9\right)$$
$$\frac{1}{2}x^{2}+3x+\frac{9}{2}$$
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$\frac{x^{2}}{2}+3x+\frac{9}{2}$
