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2n^2 - 20n + ___how do you find solve this

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2 Answers

First, factor out a 2:

2 (n2 - 10n )

Now, take half of the linear coefficient (-10) and square it (-5)2 = 25  and add this in the parentheses - HOWEVER, you have to subtract it as well:

2 (n2 - 10n + 25 - 25)

2 [(n - 5)(n - 5) - 25]

 

 

Before you can complete the square, you need the coefficient on the n2 term to be 1.  In other words, you need to divide all of you terms by 2.

After dividing by 2, you will have n2 - 10n and whatever other information is in the problem.

To find the number that needs to be added to each side, divide the coefficient on the n term by 2 and then square it.  In other words:

(10/2)2 = 52 = 25

After adding 25 to each side, you can then make the left side into a perfect square:

(n - 5)2 

Notice that the last term is the square root of what you added to each side.