Final answer:
To rewrite the equation 24 = x² - 4x + 3 by completing the square, we should isolate the quadratic and linear terms to one side and add the square of half the coefficient of x to both sides. This yields (x - 2)² = 25, which upon taking the square root gives us the solutions x = 7 or x = -3.
Step-by-step explanation:
To rewrite the equation 24 = x² - 4x + 3 by completing the square, we need to first move the constant term to the other side of the equation to set it up for completion. Then the equation becomes x² - 4x = 21. To complete the square, we need to add the square of half the coefficient of the x term to both sides of the equation (which is (-4/2)² = 4).
Add 4 to both sides to get x² - 4x + 4 = 25. Now the left side of the equation is a perfect square, and we can write it as (x - 2)² = 25. To solve for x, take the square root of both sides, leading to x - 2 = ± 5, and then solve for x to get the solutions x = 7 or x = -3.