Solving Quadratic Equations by Completing the Square

This video tutorial teaches how to solve quadratic equations by completing the square, focusing on cases where the leading coefficient is 1. It explains the concept of perfect square trinomials, how to create them from non-perfect square trinomials, and how to solve the resulting equations. The tutorial uses visual aids like tiles to represent terms and demonstrates the process of transforming and solving the equation step-by-step.

What is a perfect square trinomial?

• A trinomial that can be factored into two different binomials.

• A trinomial that can be factored into a single binomial squared.

• A trinomial with no constant term.

• A trinomial that cannot be factored.

How can you create a perfect square trinomial from a non-perfect square trinomial?

• By dividing the entire equation by the linear term.

• By multiplying the quadratic term by 2.

• By subtracting the square of the constant term.

• By adding the square of half the coefficient of the linear term.

What is the first step in completing the square for the equation x^2 + 8x - 33 = 0?

• Move the constant term to the other side of the equation.

• Subtract 8x from both sides.

• Add 33 to both sides.

• Divide the entire equation by 2.

After completing the square, what is the next step to solve the equation?

• Multiply both sides by the square root.

• Add the constant term back to the left side.

• Factor the perfect square trinomial.

• Divide both sides by the linear term.

What are the possible solutions for the equation after factoring the perfect square trinomial?

• x = 3 or x = -11

• x = 7 or x = -7

• x = 4 or x = -4

• x = 0 or x = -8