SOLUTION: please help me solve this equation. directions i was given: use the quadratic formula to solve the equation. x^2-x+1=0

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Question 174719: please help me solve this equation.
directions i was given:
use the quadratic formula to solve the equation.
x^2-x+1=0
Found 2 solutions by Mathtut, jim_thompson5910:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-x%2B1
:
system%281%2F2%2B%28sqrt%283%29%2F2%29i%2C1%2F2-%28sqrt%283%29%2F2%29i%29
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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 , or
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 jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-x%2B1=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-1, and c=1


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-1, and c=1


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%281%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4+%29%29%2F%282%281%29%29 Multiply 4%281%29%281%29 to get 4


x+=+%281+%2B-+sqrt%28+-3+%29%29%2F%282%281%29%29 Subtract 4 from 1 to get -3


x+=+%281+%2B-+sqrt%28+-3+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+i%2Asqrt%283%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%281%2Bi%2Asqrt%283%29%29%2F%282%29 or x+=+%281-i%2Asqrt%283%29%29%2F%282%29 Break up the expression.


So the answers are x+=+%281%2Bi%2Asqrt%283%29%29%2F%282%29 or x+=+%281-i%2Asqrt%283%29%29%2F%282%29


which approximate to x=0.5%2B0.866i or x=0.5-0.866i