Solve the given quadratic equation by completing the square.
$3x^2-6x-9=0$

• A. $x=3,x=-1$
• B. $x=3,x=1$
• C. $x=2,x=3$
• D. $x=-3,x=-4$

Answer: (A)

Verified step by step guidance

1. Start by moving the constant term to the other side of the equation: 3x^2 - 6x = 9.
2. Divide the entire equation by 3 to simplify: x^2 - 2x = 3.
3. To complete the square, take half of the coefficient of x, which is -2, divide it by 2 to get -1, and then square it to get 1. Add and subtract this square inside the equation: x^2 - 2x + 1 - 1 = 3.
4. Rewrite the equation as a perfect square trinomial: (x - 1)^2 - 1 = 3.
5. Add 1 to both sides to isolate the perfect square: (x - 1)^2 = 4. Then, take the square root of both sides and solve for x: x - 1 = ±2, leading to x = 3 or x = -1.