Solve the quadratic equation
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}
      2 

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

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