Quadratic Equations: Completing the Square

This video tutorial explains how to solve quadratic equations by completing the square. It begins with an introduction to the square root principle and then details the steps involved in completing the square. The video includes three examples: a basic quadratic equation, one involving fractions, and a more complex equation. Each example demonstrates the process of transforming the equation into a perfect square trinomial and solving for x. The tutorial concludes by highlighting the usefulness of this method for non-factorable quadratic equations.

What is the first step in solving a quadratic equation using the square root principle?

• Take the square root of both sides

• Square both sides of the equation

• Add a constant to both sides

• Multiply both sides by a constant

When completing the square, what should you do if the leading coefficient is not one?

• Divide every term by the leading coefficient

• Ignore the leading coefficient

• Add the leading coefficient to both sides

• Multiply every term by the leading coefficient

In the first example, what is the value added to both sides to complete the square?

• 6

• 9

• 12

• 3

What is the purpose of showing the calculation of 12b^2 in the second example?

• To simplify the equation

• To make factoring easier, especially with fractions

• To eliminate fractions from the equation

• To find the roots of the equation

In the second example, what is the result of adding -10 and 25/4?

• -5/4

• -10

• -15/4

• -5

In the final example, what is the first step after adding nine to both sides?

• Multiply every term by three

• Divide every term by three

• Add three to both sides

• Subtract three from both sides

What is the simplified form of the square root of 28?

• 2√7

• 4√7

• √28

• 3√7

In the final example, what is the common denominator used to combine 3 and 1/9?

• 1

• 27

• 3

• 9

What is the final form of the solution in the last example?

• 1/3 plus or minus 2√7 all over 3

• -1 plus or minus 2√7 all over 3

• 1/3 plus or minus √7 all over 3

• -1 plus or minus √7 all over 3

What is the main advantage of completing the square for solving quadratic equations?

• It is faster than other methods

• It works for equations that are not factorable

• It always gives integer solutions

• It eliminates the need for a calculator