Final answer:
To solve the equation by completing the square, we rearrange the terms and then add the square of half of the coefficient of x to both sides. By rewriting the left side of the equation as a perfect square, we can solve for x by taking the square root. The correct answer is x = 3.
Step-by-step explanation:
To solve the given equation by completing the square, we need to move all the terms to one side so that the equation is in the form ax² + bx + c = 0. The equation is 3x² - 15x = 48 - 3x. Rearranging the terms, we get 3x² - 15x + 3x = 48. Simplifying further, we have 3x² - 12x = 48.
To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation. Half of -12 is -6, so we add (-6)² = 36 to both sides.
The equation becomes 3x² - 12x + 36 = 48 + 36. Simplifying, we have 3x² - 12x + 36 = 84.
We can now rewrite the left side of the equation as a perfect square.
The expression (x - 2)² is equal to x² - 4x + 4. To make it equal to the left side of the equation, we multiply it by 3.
We have 3(x - 2)² = 84. Dividing both sides by 3, we get (x - 2)² = 28.
Taking the square root of both sides, we have x - 2 = ±√28. Simplifying, x - 2 = ±2√7.
Finally, solving for x, we get x = 2 ± 2√7. This gives us two possible solutions: x = 2 + 2√7 and x = 2 - 2√7.
Therefore, the correct answer is B) x = 3.