Final answer:
To rewrite the equation by completing the square, add the square of half the coefficient of the x-term to both sides. The equation (x - 2)^2 = 27 is the correct rewritten equation. The solutions to the equation are x = 2 ± √27.
Step-by-step explanation:
To rewrite the equation by completing the square, we want to make the quadratic expression on the left side of the equation a perfect square trinomial. We can do this by adding the square of half the coefficient of the x-term to both sides of the equation.
Here's how:
24 = x^2 - 4x + 3
24 + (4/2)^2 = x^2 - 4x + 3 + (4/2)^2
24 + 4 = x^2 - 4x + 4 + 3
28 = (x - 2)^2 + 3
So the rewritten equation is (x - 2)^2 = 25.
The correct answer choice is B) (x - 2)^2 = 27.
To find the solutions to the equation, we can take the square root of both sides:
√[(x - 2)^2] = ±√27
x - 2 = ±√27
x = 2 ± √27