1. Equations and Inequalities

Completing the Square

1. Equations and inequalities

Completing the Square

Struggling with Precalculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

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 by moving 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 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.

Rewrite the equation as a perfect square trinomial: (x - 1)^2 - 1 = 3.

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.