Solve by completing the square?

x^2 - 2x = 24

Since the coefficient of the x^2 term is 1, we need only take half of the coefficient of the x term, square it, and add that to both sides of the equation:
x^2 - 2x + (-2/2)^2 = 24 + (-2/2)^2
x^2 - 2x + 1 = 24 + 1
(x - 1)^2 = 25
(x - 1) = +/- 5
x = 1 +/- 5
x = 6 or x = -4

Completing the square is actually pretty easy.

1) Make sure the x^2 term is 1 (it is in this case)
2) Move the constant to the right side (it is in this case)
3) Take half the x coefficient (-2/2) and square it (1), add this to both sides.

x^2 - 2x + 1 = 24 + 1

4) Complete the square (the half value calculated in step 3 will be part of the answer)

(x - 1)^2 = 25

Take the square root of both sides to get x - 1 = 5, or x= 6 and x -1 = -5 or x = -4

x² - 2x + 1 = 25
(x - 1)² = 25
(x - 1) = ± 5
x = 1 ± 5
x = 6 , x = - 4

OPTION D

x^2 - 2x = 24
x^2 - 2x - 24 = 0
(x - 1)^2 - 25 = 0
(x - 1)^2 = 25
x - 1 = ±√25
x - 1 = ±5

x - 1 = 5
x = 6

x - 1 = -5
x = -4

∴ x = 6 , -4
(answer D)