Mastering the Complete the Square Method for Quadratic Equations

Mr. Boyd teaches how to solve quadratic equations by completing the square. The lesson covers the steps involved, including moving the constant, completing the square, factoring, and isolating the variable. Several examples are provided to illustrate the method, including cases with non-unit coefficients. The video concludes with a summary and encouragement to subscribe for more tutorials.

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

• Factor the quadratic equation

• Move the constant to the other side of the equation

• Add the constant to both sides

• Take the square root of both sides

In the process of completing the square, what do you add to both sides of the equation?

• The square of the constant term

• The constant term

• The square of half the coefficient of x

• The coefficient of x

In the first example, what is the value added to both sides after dividing the coefficient of x by 2 and squaring it?

• 25

• 16

• 9

• 4

What are the solutions to the equation x^2 - 6x + 9 = 25 after completing the square?

• x = 3 ± 6

• x = 3 ± 4

• x = 3 ± 5

• x = 3 ± 7

In the second example, what is the constant term moved to the other side of the equation x^2 + 22x + 21 = 0?

• 21

• 1

• 22

• 0

What is the result of taking the square root of both sides in the equation x^2 + 22x + 121 = 100?

• x + 11 = ± 10

• x + 11 = ± 11

• x + 10 = ± 11

• x + 10 = ± 10

In the third example, what is the approximate value of the square root of 6?

• 2.54

• 2.64

• 2.44

• 2.24

What are the solutions to the equation x^2 - 2x + 1 = 6 after completing the square?

• x = 1 ± 2.74

• x = 1 ± 2.44

• x = 1 ± 2.64

• x = 1 ± 2.54

In the fourth example, what is the constant term added to both sides of the equation x^2 + 10x - 4 = 0?

• 4

• 5

• 7

• 6

What is the final solution to the equation x^2 - 4x + 3 = 0 after completing the square and simplifying?

• 0.29 or 3.71

• 0.19 or 3.81

• 0.39 or 3.61

• 0.09 or 3.91