Completing the Square Techniques

Nancy explains how to solve quadratic equations by completing the square, covering three cases: positive x^2, coefficients greater than 1, and negative coefficients. She provides step-by-step instructions, highlights common mistakes, and offers tips for avoiding errors. The video emphasizes the importance of balancing equations and remembering to consider both positive and negative solutions when taking square roots.

What is the main reason for using the completing the square method?

• It is the fastest method for solving quadratic equations.

• It always provides a single solution.

• It is the only method that works for all quadratic equations.

• It transforms the equation into a perfect square form.

In the first case, what is the initial step when completing the square for an equation starting with x^2?

• Add a number to both sides to balance the equation.

• Square root both sides of the equation.

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

• Divide all terms by the coefficient of x^2.

How do you determine the number to add to both sides in the first case?

• Add the coefficient of x to the constant term.

• Double the coefficient of x.

• Square the constant term.

• Divide the coefficient of x by 2 and square it.

What is the first step when dealing with an equation where the coefficient of x^2 is greater than 1?

• Add the coefficient to the constant term.

• Divide all terms by the coefficient of x^2.

• Subtract the coefficient from the x term.

• Multiply all terms by the coefficient of x^2.

In the second case, what must be done after dividing all terms by the coefficient of x^2?

• Add the constant term to both sides.

• Square root both sides of the equation.

• Add a number to both sides to form a perfect square.

• Multiply the x term by the coefficient.

What is the first step when the equation starts with a negative x^2 term?

• Subtract the x term from both sides.

• Add the constant term to the left side.

• Divide all terms by -1 to make x^2 positive.

• Multiply all terms by -1 to make x^2 negative.

In the third case, what is the purpose of dividing all terms by -1?

• To simplify the equation.

• To make the x term negative.

• To eliminate the constant term.

• To make the x^2 term positive.

What is a common mistake when solving by completing the square?

• Not multiplying the x term by the coefficient.

• Not dividing the coefficient of x by 2.

• Forgetting to add the constant term to both sides.

• Forgetting to include both positive and negative solutions.

Why can't you complete the square if there is no x term?

• The x^2 term is negative.

• There is no constant term to move.

• The equation is already in perfect square form.

• There is no coefficient to divide by 2 and square.

What should you do if completing the square is not applicable?

• Multiply all terms by the coefficient of x^2.

• Use the quadratic formula or factoring.

• Divide all terms by the constant term.

• Add a constant term to both sides.