Solving Quadratic Equations by Completing the Square with Non-Unit Leading Coefficient

This lesson teaches how to solve quadratic equations by completing the square, especially when the leading coefficient is not 1. It explains the concept of perfect square trinomials and how to transform non-perfect squares into perfect squares by identifying and adding the missing component. The lesson provides a detailed example of solving a quadratic equation with a non-unit leading coefficient, demonstrating the process of dividing to simplify the equation, completing the square, and solving for the variable.

What is the purpose of completing the square in a quadratic equation?

• To eliminate the x term

• To turn it into a perfect square trinomial

• To find the roots directly

• To simplify the equation

When the leading coefficient is not 1, what is the first step in completing the square?

• Add the leading coefficient to all terms

• Multiply all terms by the leading coefficient

• Divide all terms by the leading coefficient

• Subtract the leading coefficient from all terms

In the example problem, what is the value of the b term after dividing by 2?

• 1/2

• 3/2

• 3/4

• 9/16

What is the next step after forming a perfect square trinomial?

• Add the same value to both sides

• Factor the trinomial

• Multiply the trinomial by 2

• Subtract the trinomial from both sides

What operation is used to solve the equation after completing the square?

• Addition

• Multiplication

• Square root

• Subtraction

What are the possible solutions for x after taking the square root?

• x = 0 or x = 2

• x = 1/2 or x = -2

• x = 2 or x = -1/2

• x = 1 or x = -1

Why is it necessary to consider both positive and negative roots when solving the equation?

• Because it eliminates the x term

• Because it simplifies the equation

• Because the square root can be positive or negative

• Because the equation is quadratic