SOLUTION: -16tē + 30t + 8 = 0

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Question 172108: -16tē + 30t + 8 = 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
-16tē + 30t + 8 = 0
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8tē - 15t - 4 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B-15x%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=%28-15%29%5E2-4%2A8%2A-4=353.

Discriminant d=353 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--15%2B-sqrt%28+353+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+353+%29%29%2F2%5C8+=+2.1117683892535
x%5B2%5D+=+%28-%28-15%29-sqrt%28+353+%29%29%2F2%5C8+=+-0.236768389253496

Quadratic expression 8x%5E2%2B-15x%2B-4 can be factored:
8x%5E2%2B-15x%2B-4+=+%28x-2.1117683892535%29%2A%28x--0.236768389253496%29
Again, the answer is: 2.1117683892535, -0.236768389253496. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-15%2Ax%2B-4+%29

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The answers are correct, but ignore the factors.