Which value must be added to the expression x^2+x to make it a perfect trinomial

answer:

1/9

step-by-step explanation:

to answer this, we "complete the square."

start with x^2+x.

1. identify the coefficient of the x term; it is 1.

2. halve this result, obtaining 1/2, and then square the latter:   (1/2)² = 1/4

3.   add 1/4 to, and then subtract 1/4 from, the original x^2+x:

      x^2+x + 1/4 - 1/4 this is exactly equivalent to   x^2+x.

4.   strictly speaking, the answer to this problem is 1/4, since adding 1/4 to  

x^2+x makes x^2+x into a perfect square.