SOLUTION: X^2 + x +1 = 0

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Question 1083580: X^2 + x +1 = 0
Found 2 solutions by KMST, Alan3354:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Equations are solved by finding easier equivalent equations.
Equivalent equations are equations that have exactly the same solutions.
The equations listed below are all equivalent.
x%5E2%2Bx%2B1=0
x%5E2%2Bx%2B1%2F4%2B3%2F4=0%7D%7D%0D%0A%7B%7B%7B%28x%2B1%2F2%29%5E2%2B3%2F4=0
There is no real solution to those equations.
For all real values of x,
%28x%2B1%2F2%29%5E2%3E=0 and %28%2B1%2F2%29%2B3%2F4%3E=3%2F4 .
If you are looking for complex solutions,
%28x%2B1%2F2%29%5E2=-3%2F4 ,
x%2B1%2F2=%22+%22+%2B-+i%2Asqrt%283%29%2F2 , and
x=-1%2F2+%2B-+i%2Asqrt%283%29%2F2

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
X^2 + x +1 = 0
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Thx for letting us know.
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If you want to solve for x, you should say, "Solve for x."
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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 1x%5E2%2B1x%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=%281%29%5E2-4%2A1%2A1=-3.

The discriminant -3 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 -3 is + or - sqrt%28+3%29+=+1.73205080756888.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B1+%29