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

Question

cpmpleting the square

Answer 1

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]

 

 

Answer 2

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.