Completing the Square Concepts

This video tutorial explains how to solve quadratic equations that cannot be factored using the method of completing the square. It begins with an introduction to the problem and reviews the concept of perfect square trinomials. The tutorial then provides a detailed, step-by-step guide on how to complete the square to solve a quadratic equation, emphasizing the importance of balancing equations. Common mistakes are highlighted to help learners avoid errors.

What is the main challenge in solving the equation x^2 + 16x - 22 = 0 by factoring?

• Finding the square root of 22

• Balancing the equation

• Completing the square

• Finding two numbers that multiply to -22 and add to 16

What is the first step in creating a perfect square trinomial from a binomial?

• Multiply the coefficient of the second term by 2

• Divide the coefficient of the second term by 2

• Subtract 8 from both sides

• Add 22 to both sides

What constant term should be added to x^2 + 16x to make it a perfect square trinomial?

• 8

• 22

• 16

• 64

After completing the square, what is the equation x^2 + 16x + 64 factored into?

• (x + 4)^2

• (x - 8)^2

• (x - 4)^2

• (x + 8)^2

What is the next step after factoring the equation into (x + 8)^2 = 86?

• Take the square root of both sides

• Subtract 8 from both sides

• Add 8 to both sides

• Multiply both sides by 2

What should you remember when taking the square root of both sides of an equation?

• Ignore the roots

• Consider both positive and negative roots

• Only consider the negative root

• Only consider the positive root

What is the final expression for x after solving the equation?

• x = ±√22 - 8

• x = ±√22 + 8

• x = ±√86 - 8

• x = ±√86 + 8

What is a common mistake when completing the square?

• Multiplying the constant term by 2

• Subtracting the constant term from both sides

• Adding the constant term to both sides

• Forgetting to add the constant term to both sides

What happens if you only add the constant term to one side of the equation?

• The equation is solved correctly

• The equation becomes unbalanced

• The equation becomes a perfect square

• The equation remains balanced

Why is it important to balance the equation when completing the square?

• To ensure the equation is solvable

• To maintain equality on both sides

• To make the equation a perfect square

• To simplify the equation