Completing the Square: Key Concepts and Techniques

This video tutorial covers solving quadratic equations using the method of completing the square. It includes four examples, each demonstrating different scenarios such as equations with negative coefficients and those without a middle term. The tutorial provides a step-by-step guide to solving these equations, emphasizing the importance of understanding the process of completing the square and the introduction of plus or minus when taking square roots.

What is the method called that is used to solve quadratic equations by transforming them into a perfect square trinomial?

• Factoring

• Graphing

• Completing the Square

• Quadratic Formula

In the equation x^2 + 8x - 9 = 0, what is the first step to start solving it by completing the square?

• Divide the equation by 2

• Subtract 8x from both sides

• Add 9 to both sides

• Multiply the equation by 2

After adding 16 to both sides in the equation x^2 + 8x + 16 = 25, what is the next step?

• Multiply by 2

• Subtract 16 from both sides

• Take the square root of both sides

• Divide by 2

In the equation 2x^2 - 6x - 5 = 0, what should you do to make the coefficient of x^2 equal to 1?

• Multiply by 2

• Subtract 6x from both sides

• Divide by 2

• Add 5 to both sides

When solving 2x^2 - 6x - 5 = 0, what is the result of squaring -3/2?

• 9/4

• 1/4

• 3/4

• 6/4

In the equation -x^2 + 4x + 12 = 0, what is the first step to start solving it by completing the square?

• Add 12 to both sides

• Subtract 4x from both sides

• Divide by -1

• Multiply by -1

After adding 4 to both sides in the equation x^2 - 4x + 4 = 16, what is the next step?

• Multiply by 2

• Divide by 2

• Take the square root of both sides

• Subtract 4 from both sides

In the equation 5x^2 - 125 = 0, what is the first step to start solving it?

• Divide by 5

• Subtract 125 from both sides

• Multiply by 5

• Add 125 to both sides

What is the result of dividing 125 by 5 in the equation 5x^2 = 125?

• 25

• 20

• 15

• 30

When solving 5x^2 - 125 = 0, what is the final step to find the value of x?

• Take the square root of both sides

• Add 5 to both sides

• Subtract 5 from both sides

• Multiply by 5