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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Since we're trying to make n%5E2%2B14n%2Bc a perfect square, this means %28a%2Bb%29%5E2=n%5E2%2B14n%2Bc


a%5E2%2B2ab%2Bb%5E2=n%5E2%2B14n%2Bc Foil %28a%2Bb%29%5E2

Since we know that the first term on the right is n%5E2, this means a%5E2=n%5E2 which tells us that a=n


n%5E2%2B2nb%2Bb%5E2=n%5E2%2B14n%2Bc Plug in a=n


So this means that 2nb=14n (notice how both of these terms only have 1 "n") and b%5E2=c (notice how both of these terms have no "n" terms)


So let's use 2nb=14n to solve for b


2nb=14n Start with the given equation


cross%282n%2F2n%29b=14n%2F2n Divide both sides by 2n to isolate b



b=7 Divide





n%5E2%2B14n%2B7%5E2 Now plug in b=7 into the original polynomial n%5E2%2B14n%2Bc



n%5E2%2B14n%2B49 Now square 7 to get 49


So this means that the perfect square is n%5E2%2B14n%2B49



Check:


Notice how if we factor n%5E2%2B14n%2B49 we get %28n%2B7%29%5E2 which shows us that n%5E2%2B14n%2B49 is a perfect square. So our answer is verified.