Question 49408
To make this binomial {{{x^2+5x}}} into a perfect square trinomial, simply add the square of half the coefficient of the x-term. So you would add: {{{(5/2)^2 = 25/4}}} 

The trinomial becomes:
{{{x^2+5x+25/4}}} If you now factor this, you can see that it is a perfect square.

{{{x^2+5x+25/4 = (x+5/2)^2}}} Check using FOIL.
{{{(x+5/2)(x+5/2) = x^2+(5/2)x+(5/2)x+25/4}}} Simplify to: {{{x^2+5x+25/4}}}