SOLUTION: Solve 27 - 3x= 2x squared

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Question 145419: Solve 27 - 3x= 2x squared
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
27+-+3x=+2x%5E2
2x%5E2+%2B+3x+-+27+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B3x%2B-27+=+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=%283%29%5E2-4%2A2%2A-27=225.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+225+%29%29%2F2%5C2+=+3
x%5B2%5D+=+%28-%283%29-sqrt%28+225+%29%29%2F2%5C2+=+-4.5

Quadratic expression 2x%5E2%2B3x%2B-27 can be factored:
2x%5E2%2B3x%2B-27+=+%28x-3%29%2A%28x--4.5%29
Again, the answer is: 3, -4.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-27+%29