SOLUTION: solve for quadratic 3x2 - x = 11

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Question 672328: solve for quadratic 3x2 - x = 11
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3x2 - x = 11
3x2 - x - 11 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-1x%2B-11+=+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=%28-1%29%5E2-4%2A3%2A-11=133.

Discriminant d=133 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+133+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+133+%29%29%2F2%5C3+=+2.08876043244513
x%5B2%5D+=+%28-%28-1%29-sqrt%28+133+%29%29%2F2%5C3+=+-1.7554270991118

Quadratic expression 3x%5E2%2B-1x%2B-11 can be factored:
3x%5E2%2B-1x%2B-11+=+%28x-2.08876043244513%29%2A%28x--1.7554270991118%29
Again, the answer is: 2.08876043244513, -1.7554270991118. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-1%2Ax%2B-11+%29