SOLUTION: 2x^2- 2/3x - 1/6 =0 answer: x= -1/6 or 1/2 need a break down of why my text book got this answer

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Question 181797: 2x^2- 2/3x - 1/6 =0

answer: x= -1/6 or 1/2

need a break down of why my text book got this answer
Found 2 solutions by Alan3354, nerdybill:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2- 2/3x - 1/6 =0
answer: x= -1/6 or 1/2
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2x^2- 2/3x - 1/6 =0
Multiply by 6 to get rid of fractions.
12x^2 - 4x - 1 = 0
Here, you can factor or use the quadratic equation.
(6x + 1)*(2x - 1) = 0
6x+1 = 0 --> x = -1/6
2x-1 = 0 --> x = 1/2
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Using the onsite solver:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B-4x%2B-1+=+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=%28-4%29%5E2-4%2A12%2A-1=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+64+%29%29%2F2%5C12+=+0.5
x%5B2%5D+=+%28-%28-4%29-sqrt%28+64+%29%29%2F2%5C12+=+-0.166666666666667

Quadratic expression 12x%5E2%2B-4x%2B-1 can be factored:
12x%5E2%2B-4x%2B-1+=+%28x-0.5%29%2A%28x--0.166666666666667%29
Again, the answer is: 0.5, -0.166666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B-4%2Ax%2B-1+%29

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Note that the solver gets the right answers and it shows a graph, BUT, if the coefficient of the x^2 term is not 1, it gets the factors wrong.




Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2- 2/3x - 1/6 =0
multiply both sides by 6:
12x^2- 4x - 1 =0
Factoring:
(6x+1)(2x-1) = 0
.
Setting each term to zero yields:
(6x+1)=0
6x = -1
x = -1/6
.
(2x-1)=0
2x=1
x = 1/2