Question

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial: x^2+x+____

Answer 1

Look at your coefficient for the x term. Call that b.
You always want your constant term to be (1/2 * b)^2.
In your example b is 1

Answer 2

think of it this way
(x+k)^2 = x^2 + 2kx + k^2

we want 2k = 1
thus k = 1/2

so (1/2)^2 = 1/4

so you want to add 1/4

x^2 + x + 1/4 = (x + 1/2)^2