SOLUTION: 2a squared -9a -5 =0

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Question 297222: 2a squared -9a -5 =0
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aa%5E2%2Bba%2Bc=0 (in our case 2a%5E2%2B-9a%2B-5+=+0) has the following solutons:

a%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=%28-9%29%5E2-4%2A2%2A-5=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+121+%29%29%2F2%5Ca.

a%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+121+%29%29%2F2%5C2+=+5
a%5B2%5D+=+%28-%28-9%29-sqrt%28+121+%29%29%2F2%5C2+=+-0.5

Quadratic expression 2a%5E2%2B-9a%2B-5 can be factored:
2a%5E2%2B-9a%2B-5+=+2%28a-5%29%2A%28a--0.5%29
Again, the answer is: 5, -0.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-9%2Ax%2B-5+%29