SOLUTION: Hello, I need some help on finding the value of c that makes each trinomial a perfect square. The problem is; [n^2+14n+c] I have tried the formula: [(a+b)^2=a^2+2ab+b^2] But I s

Question 118450: Hello, I need some help on finding the value of c that makes each trinomial a perfect square. The problem is;
[n^2+14n+c]
I have tried the formula: [(a+b)^2=a^2+2ab+b^2]
But I seem to be getting stuck trying to find the value of [b]
May someone show me how to work out the problem?
Thank you :]
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since we're trying to make a perfect square, this means

Foil

Since we know that the first term on the right is , this means which tells us that

Plug in

So this means that (notice how both of these terms only have 1 "n") and (notice how both of these terms have no "n" terms)

So let's use to solve for b

Start with the given equation

Divide both sides by 2n to isolate b

Divide

Now plug in into the original polynomial

Now square 7 to get 49

So this means that the perfect square is

Check:

Notice how if we factor we get which shows us that is a perfect square. So our answer is verified.
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