Completing the Square Techniques

The video tutorial introduces a no-thinking method for completing the square, emphasizing a step-by-step approach. It covers the process of ensuring the leading coefficient is one, moving constants, and using the square root property. Two examples are provided: one with real numbers and another involving complex numbers, demonstrating the method's application.

What is the main benefit of the no-nonsense, no-thinking approach to completing the square?

• It simplifies the process by reducing the need to think.

• It guarantees correct answers every time.

• It eliminates the need for understanding.

• It requires no calculations.

What is the first step in the method for completing the square?

• Square the middle coefficient.

• Subtract the constants from both sides.

• Make the leading coefficient one.

• Add the middle coefficient to both sides.

In the first example, what is the middle coefficient divided by two?

• 4

• -4

• -8

• 8

What is the result of squaring the middle coefficient divided by two in the first example?

• 8

• 16

• 4

• 32

What is the final form of the equation on the left side after completing the square in the first example?

• (x - 8)^2

• (x + 4)^2

• (x + 8)^2

• (x - 4)^2

What is the solution for x in the first example after applying the square root property?

• 4 ± √15

• 8 ± √16

• 8 ± √15

• 4 ± √16

In the second example, what must be done first if the leading coefficient is not one?

• Square the middle coefficient.

• Add the middle coefficient to both sides.

• Divide everything by the leading coefficient.

• Subtract the constants from both sides.

What is the middle coefficient divided by two in the second example?

• 1/4

• -1/4

• 1/2

• -1/2

What is the result of squaring the middle coefficient divided by two in the second example?

• 1/32

• 1/8

• 1/16

• 1/4

What is the final solution for x in the second example?

• 1/4 ± 1/4i

• 1/2 ± 1/2i

• 1/4 ± 1/2i

• 1/2 ± 1/4i