SOLUTION: Need to solve quadratic equation using any appropriate method. x^2/10 - x/5 + 2 = 0 What method can be used? How do you solve?

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Question 26483: Need to solve quadratic equation using any appropriate method. x^2/10 - x/5 + 2 = 0 What method can be used? How do you solve?
Answer by stanbon(48568) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply through by 10 to get:
x^2-2x+20=0
Use the quadratic formula to get:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B20+=+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=%28-2%29%5E2-4%2A1%2A20=-76.

The discriminant -76 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 -76 is + or - sqrt%28+76%29+=+8.71779788708135.

The solution is x%5B12%5D+=+%28--2%2B-+i%2Asqrt%28+-76+%29%29%2F2%5C1+=++%28--2%2B-+i%2A8.71779788708135%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B20+%29

Cheers,
Stan H.