Completing the Square in Quadratics

This video tutorial explains how to solve quadratic equations by completing the square. It assumes prior knowledge of the five steps involved in the process. The tutorial walks through moving the constant to the right side, creating a perfect square trinomial, factoring, and solving the equation. The example concludes with finding two real irrational solutions.

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

• Move the constant to the left side of the equation.

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

• Add a constant to both sides of the equation.

• Factor the equation immediately.

When moving the constant to the right side, what operation is performed?

• Multiplication

• Division

• Addition

• Subtraction

What is the formula to find the constant term needed to make a perfect square trinomial?

• B times 2 squared

• B divided by 2 squared

• B squared

• B divided by 4

In the example, what is the value of B?

• 5

• 10

• 25

• 2

What is the constant added to both sides to complete the square in the example?

• 5/2

• 25/4

• 10/4

• 5

What is the result of factoring the trinomial in the example?

• (x + 5/2)(x + 5/2)

• (x + 5)(x + 5)

• (x + 2.5)(x + 2.5)

• (x + 5/4)(x + 5/4)

What is the equation after factoring and simplifying?

• (x + 5/2)^2 = 17/4

• (x + 5)^2 = 17/4

• (x + 2.5)^2 = 17/4

• (x + 5/4)^2 = 17/4

What operation is used to solve for x after factoring?

• Multiplication

• Subtraction

• Addition

• Taking the square root

What are the two solutions for x in the example?

• -5 ± √17

• -5/2 ± √17

• -5 ± √17/2

• -5/2 ± √17/2

What type of solutions are obtained in the example?

• Two real irrational solutions

• One real and one imaginary solution

• Two imaginary solutions

• Two real rational solutions