SOLUTION: solve x2 - x + 1 I tried by using quadratic formula.

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Question 468507: solve x2 - x + 1
I tried by using quadratic formula.
Found 2 solutions by jorel1380, algebrahouse.com:
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%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=%28-1%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

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B1+%29

Answer by algebrahouse.com(1659) About Me  (Show Source):
You can put this solution on YOUR website!
x² - x + 1 = 0
a = 1, b = -1, c = 1

-b ± √(b² - 4ac)
---------------- = x {the quadratic formula}
2a

-(-1) ± √[(-1)² - 4(1)(1)]
--------------------------- = x {substituted into quadratic formula}
2(1)

1 ± √(1 - 4)
------------- = x {simplified}
2

1 ± √-3
--------- = x {subtracted 1 and -4}
2

1 ± √-1 √3
----------- = x {broke the -3 into -1 and 3, because you can't take square root of negative number}
2

1 ± i√3
-------- = x {using imaginary numbers, the square root of -1 is i}
2

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