SOLUTION: solve 2sin^2x+3sinx-4=0 in the interval 0<x<pi

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Question 1035839: solve 2sin^2x+3sinx-4=0 in the interval 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
solve 2sin^2x+3sinx-4=0 in the interval 0 ----------
Solve for what?
You should say, "Solve for x."
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2sin^2x+3sinx-4=0
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Sub u for sin(x)
2u^2 + 3u - 4 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B3x%2B-4+=+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=%283%29%5E2-4%2A2%2A-4=41.

Discriminant d=41 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+41+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+41+%29%29%2F2%5C2+=+0.850781059358212
x%5B2%5D+=+%28-%283%29-sqrt%28+41+%29%29%2F2%5C2+=+-2.35078105935821

Quadratic expression 2x%5E2%2B3x%2B-4 can be factored:
2x%5E2%2B3x%2B-4+=+%28x-0.850781059358212%29%2A%28x--2.35078105935821%29
Again, the answer is: 0.850781059358212, -2.35078105935821. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-4+%29

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Ignore the negative value.
sin(x) = ????????? see above
sin(x) = 0.85078...