## Algebra: A Combined Approach (4th Edition)

$n^2+5n+\frac{25}{4}=(n+\frac{5}{2})^2$
We add the square of half of the coefficent of $n$ so that the result is a perfect square trinomial. Co-efficient of $n=5$ Half of 5 is $\frac{1}{2}×5=\frac{5}{2}$ Square of $\frac{5}{2}$ is $\frac{5}{2}×\frac{5}{2}=\frac{25}{4}$ We add $\frac{25}{4}$ to $n^2+5n$ to make it a perfect square trinomial. Hence it becomes $n^2+5n+\frac{25}{4}$ Factored form- $n^2+5n+\frac{25}{4}$ $= n^2+\frac{5}{2}n+\frac{5}{2}n +\frac{25}{4}$ $=n(n+\frac{5}{2})+\frac{5}{2} (n+\frac{5}{2})$ (Taking the common factors) $=(n+\frac{5}{2}) (n+\frac{5}{2})$ ($(n+\frac{5}{2})$ is taken common from both the terms) $=(n+\frac{5}{2})^2$