Find the constant term that should be added to make the following expression a perfect-square trinomial.?

Question

Find the constant term that should be added to make the following expression a perfect-square trinomial.

x^2 + 7x

Answer 1

Take half of the coefficient of the x term, which comes to 7/2.
Square that, which comes to 49/4.
(x + 7/2)^2 = x^2 +7x + 49/4

Answer 2

I'm taking a graduate math class and am just now appreciating how important it is to be able to 'complete the square'.

You want to add an amount to make what you have a perfect square:

x^2 + 7x +(7/2)^2 - (7/2)^2
(x+7/2)^2 - (7/2)^2

See how that works, It's a common technique to add zero in a form that gives you what you want.

Answer 3

x² + 7x + 12.25 = (x + 3.5)²

I noticed that the coefficient of the middle term (7) is the sum of 2 numbers, and since your looking for a perfect square, the number must be half the middle term (3.5). The last term is the square of the this number (3.5² = 12.25).

Answer 4

Multiply -6 by 1/2, in other words, halve it (-3) and then square that number (-3x-3=9) The constant is 9.

Answer 5

(a+b)^2 = (a+b)(a+b) a perfect square
(a+b)(a+b) =a^2 + 2ab + b^2
substitute x for a
7x = 2xb
7 = 2b
b = 7/2
b^2 = (7/2)^2 = 49/4 or 12.25

Answer 6

x^2+7x+(7/2)^2
x^2+7x+79/4

Answer 7

x^2+7x
(x+3.5)^2=x^2+7x+12.25

add 12.25