cpmpleting the square

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

# 2 Answers

First, factor out a 2:

2 (n^{2} - 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 (n^{2} - 10n + 25 - 25)

2 [(n - 5)(n - 5) - 25]

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

After dividing by 2, you will have n^{2} - 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} = 5^{2} = 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.