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