Answer:
x = 1 + (i)5 and x = 1 - (i)5
Step-by-step explanation:
x^2-2x+26=0 can be rewritten by completing the square of x^2-2x, as follows:
x^2-2x+26=0
x^2-2x+ 1 - 1 +26=0 (this 1 comes from halving the coefficient of x (which is -2), obtaining -1, squaring the result, and then adding this 1 to and subtracting this 1 from x^2-2x) → x^2-2x+ 1 - 1 +26=0
Rewriting x^2-2x+ 1 as the square of a binomial, we get:
(x - 1)² - 1 +26=0, or (x - 1)² - 1 +26=0, or (x - 1)² = -25
Taking the square root of both sides yields x - 1 = ±(i)5.
Thus, the roots are x = 1 + (i)5 and x = 1 - (i)5 (Answer C)
