Answer
$n^2+5n+\frac{25}{4}=(n+\frac{5}{2})^2$
Work Step by Step
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)
$=(n+\frac{5}{2})^2$
