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Question 180578This question is from textbook Sullivan Algebra and Trigonoetry
: f(x)=-3x^2 + 5x
If f(x)=-2, what is x? What point(s) are on the graph of f?
My understanding>>>
-2=-3x^2+5x
0=-3x^2+5x+2
Factor it (I believe this is where I am messing up)
0= (??_ ??)(??_??)
Set both to zero
0= (??_??) 0=(??_??)
Solve for each.
Am I using the right process to solve for x?
How do I factor this properly? (my signs are not comming out right when I foil my answer to check it)
How would I determine my domain after I have determined the value of x?
This question is from textbook Sullivan Algebra and Trigonoetry
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! It looks like you have a good understanding of what you are doing. It seems that the only thing that is hanging you up is the factoring.
So let's factor 
Start with the given expression.
 Factor out a negative 1 (to make the leading coefficient positive; this isn't required, but it helps)
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Now let's factor the inner expression 
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 :
1,2,3,6
-1,-2,-3,-6
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-6)
2*(-3)
(-1)*(6)
(-2)*(3)
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 | -6 | 1+(-6)=-5 | | 2 | -3 | 2+(-3)=-1 | | -1 | 6 | -1+6=5 | | -2 | 3 | -2+3=1 |
From the table, we can see that the two numbers  and add to (the middle coefficient).
So the two numbers and both multiply to and add to
Now replace the middle term  with  . Remember, and add to . So this shows us that  .
 Replace the second term with .
 Group the terms into two pairs.
 Factor out the GCF  from the first group.
 Factor out  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.
 Combine like terms. Or factor out the common term 
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So this means that factors further down to 
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Answer:
So completely factors to .
Now from here, simply set each factor equal to zero and solve for "x"
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