Answer to Question #37382 in Algebra for Fuwad

Question

Hi! It would be very kind of you if I get the answer.
What number would be needed to add to xsquare+6x to get the result of a perfect square. What method to use and how to do it? Pls.

Answer 1

x2 + 6x(1)
There is a simple formula in elementary algebra for computing the square of a binomial:
(x + p)2 =x2 + 2xp + x2. (2)
In our case we have:
x2 + 6x = x2 + 2x ∙ 3 → p = 3.
So, we clearly see from (2) that we should add p2 = 3^2 = 9 to (1) to complete square
We obtain: x2 + 6x + 9 = x2 + 2x ∙ 3 + 3^2 = (x + 3)^2
Answer: 9