Which of the following constants can be added to x2 + 2/3 x to form a perfect square trinomial?
Accepted Solution
A:
Answer: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 - 1/9Rewrite x^2 + (2/3)x + 1/9 as the square of a binomial:(x + 1/3)^2 - 1/9In review: add 1/9 to, and then subtract 1/9 from, x^2 + (2/3)x