Solve the equation by completeing the sqaure

Question

X²-X+1= 0

I'm not sure what to do once you minus the 1 over to the over. 

Answer 1

 X^2 - X +1 = 0         there is no 2 rational numbers such that  X₁ + X_{2= -1}     X1 . X2 = 1

 

 

   To solve use factoring  by perfect square:

 

    X^2 - 2 X/ 2 + 1/4 - 1/4 +1 =0

 

    ( X + 1/2 ) ^2 = -3/4

 

     X + 1/2 = ±i√3/2

 

      X = 1/2 ± i√3/2

 

   Can use Quadratic formula as well, that is driven from factoring by perfect square method of

 

     aX^2 + bX +c        X = -b/2 ±√(b^2 - 4(a)(c))

 

     X = 1/ 2 ±√([ 1^2 - 4(1)(1)] / 2 = 1/2 ±√(3 )/2