SOLUTION: Is 18x sqr + 4x -1 =0 a real solution, two real solution, or have two imaginary solutions?

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Question 585525: Is 18x sqr + 4x -1 =0 a real solution, two real solution, or have two imaginary solutions?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Is 18x sqr + 4x -1 =0 a real solution, two real solution, or have two imaginary solutions?
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18x%5E2+%2B+4x+-+1+=+0
Find the discriminant
Disc+=+b%5E2+-+4ac+=+4%5E2+-+4%2A18%2A-1+=+16+%2B+72+=+88
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If the Disc > 0, there are 2 real solutions.
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 18x%5E2%2B4x%2B-1+=+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=%284%29%5E2-4%2A18%2A-1=88.

Discriminant d=88 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+88+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+88+%29%29%2F2%5C18+=+0.149467542212413
x%5B2%5D+=+%28-%284%29-sqrt%28+88+%29%29%2F2%5C18+=+-0.371689764434635

Quadratic expression 18x%5E2%2B4x%2B-1 can be factored:
18x%5E2%2B4x%2B-1+=+%28x-0.149467542212413%29%2A%28x--0.371689764434635%29
Again, the answer is: 0.149467542212413, -0.371689764434635. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+18%2Ax%5E2%2B4%2Ax%2B-1+%29