Question 1087252: Solve the equation by factoring. Show the complete solution.
x^2+4x-8=0
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
| Solved by pluggable solver: Factoring using the AC method (Factor by Grouping) |
Looking at the expression  , we can see that the first coefficient is  , the second coefficient is  , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,4,8
-1,-2,-4,-8
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-8) = -8
2*(-4) = -8
(-1)*(8) = -8
(-2)*(4) = -8
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | -8 | 1+(-8)=-7 | | 2 | -4 | 2+(-4)=-2 | | -1 | 8 | -1+8=7 | | -2 | 4 | -2+4=2 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
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Answer:
So  doesn't factor at all (over the rational numbers).
So is prime.
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So we can't use the factoring method to solve for x
You'll have to use another method to solve for x. Other methods are completing the square, quadratic formula, and graphing to find the roots. Let me know which method you want to use (and which method you are familiar with).
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