SOLUTION: x^2/3-x-1/6 -b+-sqr rt of b^2-4ac/ 2a a=? b=-1 c=-1/6 I am stuck as to what "a" is.

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Question 159121: x^2/3-x-1/6 -b+-sqr rt of b^2-4ac/ 2a
a=? b=-1 c=-1/6
I am stuck as to what "a" is.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x^2/3-x-1/6 -b+-sqr rt of b^2-4ac/ 2a
a=? b=-1 c=-1/6
I am stuck as to what "a" is.
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If it's x%5E2%2F3+-+x+-+1%2F6, then a = 1/3
To solve it, multiply by 6
2x^2 - 6x - 1 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-6x%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=%28-6%29%5E2-4%2A2%2A-1=44.

Discriminant d=44 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+44+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+44+%29%29%2F2%5C2+=+3.1583123951777
x%5B2%5D+=+%28-%28-6%29-sqrt%28+44+%29%29%2F2%5C2+=+-0.1583123951777

Quadratic expression 2x%5E2%2B-6x%2B-1 can be factored:
2x%5E2%2B-6x%2B-1+=+%28x-3.1583123951777%29%2A%28x--0.1583123951777%29
Again, the answer is: 3.1583123951777, -0.1583123951777. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-6%2Ax%2B-1+%29

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The onsite solver doesn't handle the coefficients well, but you can figure it out from what's shown.