SOLUTION: Solve the following questions for 0. Unless otherwise specified, give all solutions as exact radian measures 20cos^2 0-5 cos 0 + 10 = 13

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Question 1036368: Solve the following questions for 0. Unless otherwise specified, give all solutions as exact radian measures
20cos^2 0-5 cos 0 + 10 = 13
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following questions for 0. Unless otherwise specified, give all solutions as exact radian measures
20cos^2 0-5 cos 0 + 10 = 13
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Sub x for the cosine
20x^2 - 5x - 3 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 20x%5E2%2B-5x%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=%28-5%29%5E2-4%2A20%2A-3=265.

Discriminant d=265 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+265+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+265+%29%29%2F2%5C20+=+0.531970514902493
x%5B2%5D+=+%28-%28-5%29-sqrt%28+265+%29%29%2F2%5C20+=+-0.281970514902493

Quadratic expression 20x%5E2%2B-5x%2B-3 can be factored:
20x%5E2%2B-5x%2B-3+=+%28x-0.531970514902493%29%2A%28x--0.281970514902493%29
Again, the answer is: 0.531970514902493, -0.281970514902493. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+20%2Ax%5E2%2B-5%2Ax%2B-3+%29

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cos = as stated above
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Use a calculator to find the principal values.
No exact solution is possible.