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

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Answer 1 · 2015-04-08T13:12:36

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,
$k = (5/2)^2 = (25)/(4)$

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