Question 877860: Solve the following quadratic equation using factoring:
28x^2 + 30x + 32 = 0
Thank you for your help!
Found 2 solutions by Alan3354, richwmiller:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Solve the following quadratic equation using factoring:
28x2 + 30x + 32 = 0
Divide by 2
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It's either
(x + p)*(14x + q) or
(2x + p)*(7x + q)
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p & q can be
1 & 16, 2 & 8, or 4 & 4
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It's trial and error.
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All the factors are +, makes it simpler.
15x is an odd number, that's a big hint.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website!
| Solved by pluggable solver: Factoring using the AC method (Factor by Grouping) |
 Start with the given expression.
 Factor out the GCF  .
Now let's try to factor the inner expression 
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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 :
1,2,4,7,8,14,16,28,32,56,112,224
-1,-2,-4,-7,-8,-14,-16,-28,-32,-56,-112,-224
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*224 = 224
2*112 = 224
4*56 = 224
7*32 = 224
8*28 = 224
14*16 = 224
(-1)*(-224) = 224
(-2)*(-112) = 224
(-4)*(-56) = 224
(-7)*(-32) = 224
(-8)*(-28) = 224
(-14)*(-16) = 224
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 | 224 | 1+224=225 | | 2 | 112 | 2+112=114 | | 4 | 56 | 4+56=60 | | 7 | 32 | 7+32=39 | | 8 | 28 | 8+28=36 | | 14 | 16 | 14+16=30 | | -1 | -224 | -1+(-224)=-225 | | -2 | -112 | -2+(-112)=-114 | | -4 | -56 | -4+(-56)=-60 | | -7 | -32 | -7+(-32)=-39 | | -8 | -28 | -8+(-28)=-36 | | -14 | -16 | -14+(-16)=-30 |
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 simply factors to
In other words,  .
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