Solve x^{2} – 2x – 24 = 0 by using completing the square. a. {-5, -1} b. {-6, 4} c. {-20, -4} d. {6, -4}

We start by rearranging the equation such that the constant term is on the right side: $$x^2 - 2x = 24$$ Next, we add the square of half the coefficient of the x-term to both sides. We can find this value by taking half of -2, which is -1, and squaring it: $$x^2 - 2x + (-1)^2 = 24 + (-1)^2$$ Simplifying: $$x^2 - 2x + 1 = 25$$ We can now factor the left side: $$(x - 1)^2 = 25$$ Taking the square root of both sides, and remembering to include both the positive and negative roots: $$x - 1 = pm 5$$ Solving for x: $$x = 1 pm 5$$ So the solution set is {?6, 4}, which is answer choice (b).