math,help

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how do i find the following:
is there a formula for this?

Problem #15
Find the constant term that should be added to make the following expression a perfect square trinomial.

x^2+7x

square a few binomials and see if you can see a pattern

e.g. (x+3)^2 = x^2 + 6x + 9
(x-7)^2 = x^2 - 14x + 49

notice the coefficient of the middle term is twice the square root of the last term

so you have to reverse the pattern

take 1/2 of the middle term number, then square it.

for your e.g.

x^2 + 7x + ???

1/2 of 7 is 7/2, which when squared is 49/4

so
x^2 + 7x
=x^2 + 7x + 49/4 - 49/4
=(x+7/2)^2 - 49/4

I added and subtracted the same number to maintain the "equality"
I assume you are learning the method of completing the square.

i am lost?

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