SOLUTION: For what value of n is 4 x^2 + 20x + n^2 = (2x + n)^2 true for any real number x?

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Question 331748: For what value of n is 4 x^2 + 20x + n^2 = (2x + n)^2 true for any real number x?
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
Subtract %282x%2Bn%29%5E2 from boths sides:
4x%5E2%2B20x%2Bn%5E2-%282x%2Bn%29%5E2
Expand out and simplify and it whittles down to
20x-4nx=0
Factor out x:
x%2820-4n%29=0
20-4n=0 when n=5.
It is true for all x when n=5.