Which of the following constants can be added to x2 + 2/3 x to form a perfect square trinomial?

Step-by-step explanation:

Next time, please be sure to share the possible answer choices.  Also, please use " ^ " to indicate exponentiation:  x^2 + (2/3)x.

Let's actually "complete the square" here:

Starting with x^2 + (2/3)x, identify the coefficient of the x term (it is 2/3).

Take half of that, which results in 2/6, or 1/3.

Square this result, obtaining (1/3)^2 = 1/9.

Add to, and then subtract from, this square:

x^2 + (2/3)x + 1/9 - 1/9

Rewrite x^2 + (2/3)x + 1/9 as the square of a binomial:

(x + 1/3)^2 - 1/9

In review:  add 1/9 to, and then subtract 1/9 from,  x^2 + (2/3)x