SOLUTION: how to factor quadratic equation: 5X^2 + 25X + 5= 0

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Question 129969: how to factor quadratic equation: 5X^2 + 25X + 5= 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


5%2Ax%5E2%2B25%2Ax%2B5 Start with the given expression.



5%28x%5E2%2B5x%2B1%29 Factor out the GCF 5.



Now let's try to factor the inner expression x%5E2%2B5x%2B1



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Looking at the expression x%5E2%2B5x%2B1, we can see that the first coefficient is 1, the second coefficient is 5, and the last term is 1.



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



Now the question is: what two whole numbers multiply to 1 (the previous product) and add to the second coefficient 5?



To find these two numbers, we need to list all of the factors of 1 (the previous product).



Factors of 1:

1

-1



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



These factors pair up and multiply to 1.

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


Now let's add up each pair of factors to see if one pair adds to the middle coefficient 5:



First NumberSecond NumberSum
111+1=2
-1-1-1+(-1)=-2




From the table, we can see that there are no pairs of numbers which add to 5. So x%5E2%2B5x%2B1 cannot be factored.



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Answer:



So 5%2Ax%5E2%2B25%2Ax%2B5 simply factors to 5%28x%5E2%2B5x%2B1%29



In other words, 5%2Ax%5E2%2B25%2Ax%2B5=5%28x%5E2%2B5x%2B1%29.