# How do you find the missing number or term to make a perfect square trinomial. y^2 + 5y + ___ ?

${\left(y + k\right)}^{2} = {y}^{2} + 2 k y + {k}^{2}$
So if we let $k = \frac{5}{2}$, we find...
${\left(y + \frac{5}{2}\right)}^{2} = {y}^{2} + 5 y + \frac{25}{4}$
$a {y}^{2} + b y + c = a {\left(y + \frac{b}{2 a}\right)}^{2} + \left(c - {b}^{2} / \left(4 a\right)\right)$