What number must be added to x2 plus 5x to complete the square?

x2 + 5x + 6¼ = (x + 2½)2 and, hence, is a perfect square.

As the co-efficient of x2 (the first term) is 1, you can safely follow this rule:

Add the square of half the co-efficient in the second term, in order to complete the square.

In this case, you take half of 5 (which is 2½) and, then, square it. This gives you your 6¼.