Question

How do you find the constant, `k`, to make the expression `x^2 + 5x +k` a perfect square trinomial?

Answer 1

A perfect (trinomial) square, with unit coefficient on the `x^2` term, is of the form:
`(x+a)^2 = x^2+2ax+a^2`

The third term (the one that does not include the `x`) is therefore
the square of (half of the coefficient of the `x` term).

That is, for our example,
`k = (5/2)^2 = (25)/(4)`