SOLUTION: find the amount of time it takes if 400=-16t^2-2t+733

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Question 438942: find the amount of time it takes if 400=-16t^2-2t+733
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
400=-16t^2-2t+733
0=-16t^2-2t+733-400
0=-16t^2-2t+333
0=16t^2+2t-333
solve by applying the quadratic formula to get:
x = {4.5, -4.625}
we can throw out the negative answer leaving
x = 4.5 seconds
.
Details of quadratic to follow:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case 16t%5E2%2B2t%2B-333+=+0) has the following solutons:

t%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=%282%29%5E2-4%2A16%2A-333=21316.

Discriminant d=21316 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+21316+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%282%29%2Bsqrt%28+21316+%29%29%2F2%5C16+=+4.5
t%5B2%5D+=+%28-%282%29-sqrt%28+21316+%29%29%2F2%5C16+=+-4.625

Quadratic expression 16t%5E2%2B2t%2B-333 can be factored:
16t%5E2%2B2t%2B-333+=+16%28t-4.5%29%2A%28t--4.625%29
Again, the answer is: 4.5, -4.625. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B2%2Ax%2B-333+%29