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?

I understand that completing the square can be a confusing concept at first. Let me explain it in a step-by-step manner.

To find the constant term that should be added to make the expression a perfect square trinomial, you can follow these steps:

Step 1: Take the coefficient of the middle term (in this case, it is 7) and divide it by 2. This gives you 7/2.
Step 2: Square the result obtained in step 1. So, (7/2)^2 = 49/4.
Step 3: Add the result obtained in step 2 as a constant term to the expression. Thus, you get x^2 + 7x + 49/4.
Step 4: Subtract the same result obtained in step 2 from the expression. This is done to maintain the equality. So, x^2 + 7x + 49/4 - 49/4 = x^2 + 7x.
Step 5: Simplify the expression if possible. In this case, x^2 + 7x can be rewritten as (x + 7/2)^2.

By following these steps, you can find the constant term that should be added to make the expression a perfect square trinomial.

Please let me know if you have any further questions or if there's anything else I can assist you with.