SOLUTION: Solve using the quadratic formula. Approximate answers to the nearest tenth. x2+3x+2=0

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Question 273660: Solve using the quadratic formula. Approximate answers to the nearest tenth. x2+3x+2=0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A1%2A2=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+-1
x%5B2%5D+=+%28-%283%29-sqrt%28+1+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B3x%2B2 can be factored:
1x%5E2%2B3x%2B2+=+1%28x--1%29%2A%28x--2%29
Again, the answer is: -1, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B2+%29

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression x%5E2%2B3x%2B2, we can see that the first coefficient is 1, the second coefficient is 3, and the last term is 2.



Now multiply the first coefficient 1 by the last term 2 to get %281%29%282%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%2B2x. Remember, 1 and 2 add to 3. So this shows us that x%2B2x=3x.



x%5E2%2Bhighlight%28x%2B2x%29%2B2 Replace the second term 3x with x%2B2x.



%28x%5E2%2Bx%29%2B%282x%2B2%29 Group the terms into two pairs.



x%28x%2B1%29%2B%282x%2B2%29 Factor out the GCF x from the first group.



x%28x%2B1%29%2B2%28x%2B1%29 Factor out 2 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%2B2%29%28x%2B1%29 Combine like terms. Or factor out the common term x%2B1



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Answer:



So x%5E2%2B3%2Ax%2B2 factors to %28x%2B2%29%28x%2B1%29.



In other words, x%5E2%2B3%2Ax%2B2=%28x%2B2%29%28x%2B1%29.



Note: you can check the answer by expanding %28x%2B2%29%28x%2B1%29 to get x%5E2%2B3%2Ax%2B2 or by graphing the original expression and the answer (the two graphs should be identical).