Solving Quadratic Equations by Completing the Square

The video tutorial explains how to solve quadratic equations by completing the square when the coefficient of x squared is one. It provides a step-by-step guide to transforming a quadratic equation into a perfect square trinomial, allowing for the use of the square roots method to find solutions. The tutorial includes multiple examples, demonstrating the process of moving constants, calculating the magic constant, factoring, and solving for x. It also covers how to simplify solutions and provides both exact and approximate answers.

What is the primary goal of completing the square in quadratic equations?

• To isolate the x term

• To create a binomial squared

• To factorize the equation

• To simplify the equation

What must be added to both sides of the equation x^2 + 4x = 12 to make it a perfect square trinomial?

• 4

• 2

• 16

• 8

After completing the square for x^2 + 4x + 4 = 16, what is the next step to find the roots?

• Simplify the equation

• Factorize the trinomial

• Apply the quadratic formula

• Use the square roots method

What value is used to complete the square in the equation x^2 - 8x = -15?

• 2

• 16

• 8

• 4

How do you solve x^2 - 8x + 16 = 1 after factoring?

• Apply the square roots method

• Use the quadratic formula

• Graph the equation

• Subtract 1 from both sides

What is the correct factorization for x^2 - 14x + 49?

• x - 7

• (x - 49)^2

• (x - 7)^2

• x - 49

What are the solutions to the equation x^2 - 18x + 81 = 2 after applying the square roots method?

• x = 9 ± sqrt(2)

• x = 9 ± sqrt(81)

• x = 9 ± 1

• x = 9 ± 2

How is the square root of 8 simplified in the context of completing the square?

• 2 sqrt(4)

• sqrt(4) * sqrt(2)

• 4 sqrt(2)

• 2 sqrt(2)

What is the exact solution for x in the equation x^2 + 8x + 16 = 75 using the square roots method?

• x = -4 ± sqrt(75)

• x = 4 ± 5 sqrt(3)

• x = -4 ± 5 sqrt(3)

• x = 4 ± sqrt(75)

What is the simplified form of the square root of 75?

• 5 sqrt(3)

• sqrt(25) * sqrt(3)

• 7.5 sqrt(2)

• 3 sqrt(25)