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

Tags

CCSS.HSA-REI.B.4B

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

Tags

CCSS.HSA-REI.B.4B

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

Tags

CCSS.HSA-REI.B.4B

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

• 2

• 16

• 8

• 4

Tags

CCSS.HSA-REI.B.4B

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

Tags

CCSS.HSA-REI.B.4B

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

• x - 7

• (x - 49)^2

• (x - 7)^2

• x - 49

Tags

CCSS.HSA.APR.C.4

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

Tags

CCSS.HSA-REI.B.4B

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)

Tags

CCSS.HSA-REI.B.4B

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)

Tags

CCSS.HSA-REI.B.4B

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)