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

$x=3,x=-1$

$x=3,x=1$

$x=2,x=3$

$x=-3,x=-4$

Verified step by step guidance

Start by dividing the entire equation by 3 to simplify it: $ x^2 - 2x - 3 = 0 $.

Move the constant term to the other side of the equation: $ x^2 - 2x = 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 $1$ to both sides of the equation to maintain equality: $ x^2 - 2x + 1 = 4 $.

Rewrite the left side as a perfect square: $(x - 1)^2 = 4$, then solve for $x$ by taking the square root of both sides and solving the resulting linear equations.

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