SOLUTION: πx2+2x+1=0 solve using the quadratic formula

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Question 622784: πx2+2x+1=0
solve using the quadratic formula

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3.14159265358979x%5E2%2B2x%2B1+=+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=%282%29%5E2-4%2A3.14159265358979%2A1=-8.56637061435916.

The discriminant -8.56637061435916 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -8.56637061435916 is + or - sqrt%28+8.56637061435916%29+=+2.92683628075763.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3.14159265358979%2Ax%5E2%2B2%2Ax%2B1+%29

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x+=+-1%2Fpi+%2B+%282%2Fpi%29%2Ai%2Asqrt%28pi+-+1%29
x+=+-1%2Fpi+-+%282%2Fpi%29%2Ai%2Asqrt%28pi+-+1%29