SOLUTION: Find, to the nearest degree, all positive values of theta less than 360° that satisfy the equation 2tan^2-2tan=3.

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Question 971820: Find, to the nearest degree, all positive values of theta less than 360° that satisfy the equation 2tan^2-2tan=3.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find, to the nearest degree, all positive values of theta less than 360° that satisfy the equation 2tan^2-2tan=3.
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Sub x for tan
2x^2 - 2x - 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-2x%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=%28-2%29%5E2-4%2A2%2A-3=28.

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

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+28+%29%29%2F2%5C2+=+1.8228756555323
x%5B2%5D+=+%28-%28-2%29-sqrt%28+28+%29%29%2F2%5C2+=+-0.822875655532295

Quadratic expression 2x%5E2%2B-2x%2B-3 can be factored:
2x%5E2%2B-2x%2B-3+=+%28x-1.8228756555323%29%2A%28x--0.822875655532295%29
Again, the answer is: 1.8228756555323, -0.822875655532295. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-2%2Ax%2B-3+%29

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tan =~ 1.8229
theta = 61, 241 degs
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tan =~ -0.8229
theta = 321, 141 degs