Question 139520: What do I solve this by factoring?
49x^2 - 14x - 3
Thanks!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Looking at  we can see that the first term is  and the last term is  where the coefficients are 49 and -3 respectively.
Now multiply the first coefficient 49 and the last coefficient -3 to get -147. Now what two numbers multiply to -147 and add to the middle coefficient -14? Let's list all of the factors of -147:
Factors of -147:
1,3,7,21,49,147
-1,-3,-7,-21,-49,-147 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -147
(1)*(-147)
(3)*(-49)
(7)*(-21)
(-1)*(147)
(-3)*(49)
(-7)*(21)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -14
| First Number | Second Number | Sum | | 1 | -147 | 1+(-147)=-146 | | 3 | -49 | 3+(-49)=-46 | | 7 | -21 | 7+(-21)=-14 | | -1 | 147 | -1+147=146 | | -3 | 49 | -3+49=46 | | -7 | 21 | -7+21=14 |
From this list we can see that 7 and -21 add up to -14 and multiply to -147
Now looking at the expression , replace  with  (notice adds up to . So it is equivalent to )
Now let's factor  by grouping:
 Group like terms
 Factor out the GCF of  out of the first group. Factor out the GCF of out of the second group
 Since we have a common term of  , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
 Set the factorization equal to zero
Now set each factor equal to zero:
 or 
 or  Now solve for x in each case
-------------------------
Answer:
So our solutions are
or
|
|
|
