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

A perfect (trinomial) square, with unit coefficient on the ${x}^{2}$ term, is of the form:
${\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$
The third term (the one that does not include the $x$) is therefore
the square of (half of the coefficient of the $x$ term).
$k = {\left(\frac{5}{2}\right)}^{2} = \frac{25}{4}$