Completing the Square in Quadratic Equations

This video tutorial focuses on solving quadratic equations by completing the square. It begins with an introduction to the method and provides several examples, including equations with positive and negative terms, fractions, and imaginary numbers. The tutorial demonstrates how to transform quadratic equations into perfect square trinomials and solve for x, offering step-by-step guidance and tips for handling more complex expressions.

What is the first step in solving the equation x^2 + 4x + 3 = z by completing the square?

• Multiply both sides by 3

• Add 3 to both sides

• Divide both sides by 3

• Subtract 3 from both sides

In the equation x^2 + 4x = 3, what number should be added to both sides to complete the square?

• 8

• 2

• 4

• 16

What is the factored form of x^2 + 6x + 9?

• (x + 3)(x + 3)

• (x + 2)(x + 2)

• (x + 4)(x + 4)

• (x + 1)(x + 1)

How do you solve x + 2^2 = 1 for x?

• Multiply both sides by 2

• Add 2 to both sides

• Subtract 2 from both sides

• Take the square root of both sides

What is the square root of 1?

• ±1

• -1

• 1

• 0

What is the simplified form of the square root of 18?

• 3√2

• 2√3

• √9

• √36

What is the decimal value of 3 + 3√2?

• 7.243

• 6.449

• 5.828

• 4.243

What is the factored form of x^2 - 7x + 15?

• (x - 5)(x - 3)

• (x - 1)(x - 15)

• (x - 2)(x - 7)

• (x - 3)(x - 5)

What is the final answer for x in the equation 3x^2 - 5x - 7 = z?

• 3 ± √3/3

• 2 ± √2/2

• 7/2 ± √11/2

• 5/6 ± √109/6

What is the simplified form of the square root of 196?

• 12

• 14

• 18

• 16