SOLUTION: 3^x2 – 10x – 8 = 0

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Question 161948: 3^x2 – 10x – 8 = 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3^x2 – 10x – 8 = 0
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Solve for x?
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-10x%2B-8+=+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=%28-10%29%5E2-4%2A3%2A-8=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+196+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+196+%29%29%2F2%5C3+=+4
x%5B2%5D+=+%28-%28-10%29-sqrt%28+196+%29%29%2F2%5C3+=+-0.666666666666667

Quadratic expression 3x%5E2%2B-10x%2B-8 can be factored:
3x%5E2%2B-10x%2B-8+=+%28x-4%29%2A%28x--0.666666666666667%29
Again, the answer is: 4, -0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-10%2Ax%2B-8+%29

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The onsite solver is handy, and makes a nice graph, but its factoring is not right when the coefficient of the x^2 term is not 1.
The factors are (3x+2)*(x-4)