SOLUTION: how would i find the answer to 8n^2+4=12n ? i subtracted the 12n and got 8n^2-12n+4=0 after that i did the gcf and got 4(2n^2-3n+1)=0 and then i got stuck

Algebra ->  Equations -> SOLUTION: how would i find the answer to 8n^2+4=12n ? i subtracted the 12n and got 8n^2-12n+4=0 after that i did the gcf and got 4(2n^2-3n+1)=0 and then i got stuck      Log On


   

Question 262063: how would i find the answer to 8n^2+4=12n
? i subtracted the 12n and got 8n^2-12n+4=0
after that i did the gcf and got 4(2n^2-3n+1)=0 and then i got stuck
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
So far so good. You need to learn how to factor.
(n-1)(2 n-1)
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression 2x%5E2-3x%2B1, we can see that the first coefficient is 2, the second coefficient is -3, and the last term is 1.



Now multiply the first coefficient 2 by the last term 1 to get %282%29%281%29=2.



Now the question is: what two whole numbers multiply to 2 (the previous product) and add to the second coefficient -3?



To find these two numbers, we need to list all of the factors of 2 (the previous product).



Factors of 2:

1,2

-1,-2



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to 2.

1*2 = 2
(-1)*(-2) = 2


Now let's add up each pair of factors to see if one pair adds to the middle coefficient -3:



First NumberSecond NumberSum
121+2=3
-1-2-1+(-2)=-3




From the table, we can see that the two numbers -1 and -2 add to -3 (the middle coefficient).



So the two numbers -1 and -2 both multiply to 2 and add to -3



Now replace the middle term -3x with -x-2x. Remember, -1 and -2 add to -3. So this shows us that -x-2x=-3x.



2x%5E2%2Bhighlight%28-x-2x%29%2B1 Replace the second term -3x with -x-2x.



%282x%5E2-x%29%2B%28-2x%2B1%29 Group the terms into two pairs.



x%282x-1%29%2B%28-2x%2B1%29 Factor out the GCF x from the first group.



x%282x-1%29-1%282x-1%29 Factor out 1 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.



%28x-1%29%282x-1%29 Combine like terms. Or factor out the common term 2x-1



===============================================================



Answer:



So 2%2Ax%5E2-3%2Ax%2B1 factors to %28x-1%29%282x-1%29.



In other words, 2%2Ax%5E2-3%2Ax%2B1=%28x-1%29%282x-1%29.



Note: you can check the answer by expanding %28x-1%29%282x-1%29 to get 2%2Ax%5E2-3%2Ax%2B1 or by graphing the original expression and the answer (the two graphs should be identical).