Quadratic Equation: Completing the Square

The video tutorial explains how to solve a quadratic equation by completing the square. It begins by rewriting the equation in a specific form and adding a constant to create a perfect square trinomial. The tutorial then demonstrates factoring the trinomial into binomial factors and solving the equation by taking the square root of both sides. An alternative method of solving by factoring is also discussed, highlighting its simplicity compared to completing the square.

What is the first step in solving a quadratic equation by completing the square?

• Add a constant to both sides.

• Factor the equation.

• Write the equation in the form of a perfect square trinomial.

• Set the equation equal to zero.

If the coefficient of x squared is not one, what should you do?

• Add the coefficient to both sides.

• Divide both sides by the coefficient.

• Subtract the coefficient from both sides.

• Multiply both sides by the coefficient.

What constant is added to both sides to make the left side a perfect square trinomial?

• The square of the coefficient of x.

• The coefficient of x.

• Half the coefficient of x.

• The square of half the coefficient of x.

What is the result of factoring the perfect square trinomial?

• Two different binomial factors.

• A single binomial factor.

• A quadratic equation.

• Two equal binomial factors.

How do you solve for x after obtaining the perfect square trinomial?

• Multiply both sides by the constant.

• Take the square root of both sides.

• Subtract the constant from both sides.

• Add the constant to both sides.

What must be included when taking the square root of both sides?

• No additional sign.

• A plus or minus sign.

• A minus sign.

• A plus sign.

What are the solutions to the equation after solving by completing the square?

• x = 0 and x = 5

• x = -1 and x = 6

• x = 2 and x = 3

• x = 1 and x = 4

What is an alternative method to solve the quadratic equation?

• Graphing the equation.

• Factoring the equation.

• Using the quadratic formula.

• Completing the square.

What is the advantage of solving the equation by factoring?

• It is more complex.

• It is faster.

• It is more accurate.

• It provides more solutions.

What are the factors of the trinomial when using the alternative method?

• x + 1 and x + 4

• x - 1 and x - 4

• x + 2 and x + 3

• x - 2 and x - 3