Solve the quadratic equation by completing the square. verify your answer graphically. (enter your answers as a comma-separated list.) x2 − 4x + 29 = 0

Please use " ^ " to indicate exponentiation:

x^2 − 4x + 29 = 0

1) Take HALF of the coefficient (-4) of the x term.  That would be -2.
2) SQUARE this result.  Answer:  4.
3)  Insert this result and its negative inside the equation after "-4x".  Result:
      
      x^2 - 4x + 4  - 4 + 29 = 0

4)  Rewrite x^2 -4x + 4 as the square of a binomial.  Result:  (x-2)^2
5)  Combine that -4 and that 29:  Result:  25.  Rewrite:

        (x -2)^2 -4 + 29 = 0   as (x-2)^2 + 25 = 0

6)  Rewrite  (x-2)^2 + 25 = 0     as   (x-2)^2 = -25
7)  Take the square root of both sides:     (x-2) = plus or minus sqrt(-25)
8)   Simplify, remembering that the sqrt of -25 is   plus or minus i*5  :

        x-2 = plus or minus i*5
9)  Solve for x:

         x = 2 plus or minus i*5