SOLUTION: can you please help me solve by completing the square of ((( x^2-x-1=0 )))

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Question 198264This question is from textbook algebra stucture and method
: can you please help me solve by completing the square of ((( x^2-x-1=0 ))) This question is from textbook algebra stucture and method

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+x+-+1+=+0
Add 1 to both sides
x%5E2+-+x+=+1
Take 1/2 of the coefficient of x,
square it, and add it to both sides
x%5E2+-+x+%2B+%28-1%2F2%29%5E2+=+1+%2B+%28-1%2F2%29%5E2
x%5E2+-+x+%2B+1%2F4+=+4%2F4+%2B+1%2F4
The left side is a perfect square
%28x+-+1%2F2%29%5E2+=+5%2F4
Take the square root of both sides
x+-+1%2F2+=+sqrt%285%29%2F2
x+=+%281+%2B-sqrt%285%29%29%2F2
So, there are 2 answers:
x+=+%281+%2B+sqrt%285%29%29%2F2
and
x+=+%281+-+sqrt%285%29%29%2F2
I checked the 2nd one on paper -OK
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