SOLUTION: For what real values of c is x^2 - 8x - 16x + c + 24x^2 the square of a binomial?

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Question 1209149: For what real values of c is x^2 - 8x - 16x + c + 24x^2 the square of a binomial?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
For what real values of c is x^2 - 8x - 16x + c + 24x^2 the square of a binomial?

First let's combine like terms:

25x%5E2-24x%2Bc

So if it is to factor as the square of a binomial, there is 
some number a such that this is an identity:

%285x+%2B+a%29%285x+%2B+a%29%22%22=%22%2225x%5E2-24x%2Bc

25x%5E2%2B10ax%2Ba%5E2%22%22=%22%2225x%5E2-24x%2Bc

So for them to be identical, we must have:

10a=-24} and a%5E2=c

a=-24%2F10=-12%2F5 and c=a%5E2=%28-12%2F5%29%5E2=144%2F25

Answer: c = 144/25

Edwin