1. Equations & Inequalities

Completing the Square

1. Equations & Inequalities

Completing the Square

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Multiple Choice

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 with the given quadratic equation: $3x^2 - 6x - 9 = 0$.

Move the constant term to the other side of the equation: $3x^2 - 6x = 9$.

Divide the entire equation by 3 to simplify: $x^2 - 2x = 3$.

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: $x^2 - 2x + 1 - 1 = 3$.

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.