SOLUTION: 60=16x+4.9x^2 solve for x

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Question 348165: 60=16x+4.9x^2
solve for x
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
*Note: Begin by muultiplying by 10. (4.9 = 49/10)
60=16x%2B4.9x%5E2
60=16x%2B%2849%2F10%29x%5E2
600=160x%2B49x%5E2
.
Simplify
0=49x%5E2+%2B+160x-600
.
solve using the Quadratic Formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 49x%5E2%2B160x%2B-600+=+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=%28160%29%5E2-4%2A49%2A-600=143200.

Discriminant d=143200 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-160%2B-sqrt%28+143200+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28160%29%2Bsqrt%28+143200+%29%29%2F2%5C49+=+2.22875263845398
x%5B2%5D+=+%28-%28160%29-sqrt%28+143200+%29%29%2F2%5C49+=+-5.49405876090296

Quadratic expression 49x%5E2%2B160x%2B-600 can be factored:
49x%5E2%2B160x%2B-600+=+49%28x-2.22875263845398%29%2A%28x--5.49405876090296%29
Again, the answer is: 2.22875263845398, -5.49405876090296. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+49%2Ax%5E2%2B160%2Ax%2B-600+%29