# Answer to Question #37382 in Algebra for Fuwad

Question #37382

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.

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.

Expert's answer

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

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

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