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 with the given quadratic equation: \(3x^2 - 6x - 9 = 0\).
2. Move the constant term to the other side of the equation: \(3x^2 - 6x = 9\).
3. Divide the entire equation by 3 to simplify: \(x^2 - 2x = 3\).
4. To complete the square, take half of the coefficient of \(x\), which is \(-2\), divide by 2 to get \(-1\), and square it to get \(1\). Add and subtract this square inside the equation: \(x^2 - 2x + 1 - 1 = 3\).
5. Rewrite the equation as a perfect square trinomial: \((x - 1)^2 - 1 = 3\). Then, solve for \(x\) by isolating the perfect square and taking the square root of both sides.