SOLUTION: Solve 2x^2-6x-3=0

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Question 176561: Solve 2x^2-6x-3=0
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2-6x-3=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-3+=+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-3=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+60+%29%29%2F2%5C2+=+3.43649167310371
x%5B2%5D+=+%28-%28-6%29-sqrt%28+60+%29%29%2F2%5C2+=+-0.436491673103709

Quadratic expression 2x%5E2%2B-6x%2B-3 can be factored:
2x%5E2%2B-6x%2B-3+=+%28x-3.43649167310371%29%2A%28x--0.436491673103709%29
Again, the answer is: 3.43649167310371, -0.436491673103709. 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-3+%29

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Ed