a perfect trinomial, if we begin by a binomial is defined as: the square of the first term, plus (or minus) the double product of the first term times the second, plus the square of the second term:
(a + b)^2 = a^2 + 2ab + b^2
We are given:
y^2 + 5y + x
we need to find x, so x is defined as a squared quantity, which is equal to the second term coefficient (5) divided by 2, and that number squared, that is:
(5/2)^2 = 25/4
that is the third term for the trinomial to be perfect.