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What are the roots of \(x^2 - 2x + 2?\)

 Oct 28, 2019
 #1
avatar+104932 
+3

x^2  - 2x  +  2  = 0    subtract 2 from both sides

 

x^2  - 2x  = - 2         complete the square on  x

 

x^2 - 2x + 1  = - 2  + 1        factor the left side and simplify

 

(x - 1)^2  =  - 1                   take both roots

 

x - 1  =  ±√(-1)

 

x -  1   = ± i          add 1 to both sides

 

x  =   1 ± i       

 

 

cool cool cool        

 Oct 28, 2019
 #2
avatar+236 
+3

We could also use the quadratic formula for this problem. Substituting 1 in for a, -2 in for b, and 2 in for c, we get that the roots of x^2-2x+2 are (2 +- √4-8)/2, or 1 +- i, like CPhill got!

 Oct 28, 2019

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