Completing the Square Techniques

The video tutorial explains the method of completing the square to solve quadratic equations. It begins with an introduction to the concept, followed by a detailed example of solving a quadratic equation using this method. The tutorial then presents a more complex example, demonstrating the process of completing the square step-by-step. The video also highlights the relationship between completing the square and the quadratic formula, emphasizing the method's utility in solving equations that are not easily factorable.

What is the primary purpose of completing the square?

• To solve exponential equations

• To solve cubic equations

• To solve quadratic equations

• To solve linear equations

Which of the following is a key step in completing the square?

• Dividing both sides by a constant

• Subtracting a constant from both sides

• Multiplying both sides by a constant

• Adding a constant to both sides

What is the result of taking the square root of both sides in the equation x + a squared = b?

• x + a = b

• x = a + b

• x = ±√b - a

• x = ±√b - a

In the example x squared plus 16x minus 57 equals 0, what value is added to both sides to complete the square?

• 16

• 64

• 57

• 8

What is the value of 'a' when completing the square for the equation x squared plus 16x?

• 4

• 8

• 16

• 32

In the complex example, what is the first step to simplify the equation 6x squared minus 7x minus 3 equals 0?

• Divide both sides by 6

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply both sides by 6

What is the value of 'a' in the complex example when completing the square for the equation x squared minus 7/6x?

• -7/12

• 7/12

• -7/6

• 7/6

What is the final solution for x in the complex example after completing the square?

• x = 3/2 or x = -1/3

• x = 1/2 or x = -1/2

• x = 2/3 or x = -2/3

• x = 1/3 or x = -1/3

What is the purpose of adding 49/144 to both sides in the complex example?

• To factor the equation

• To simplify the equation

• To balance the equation

• To complete the square

What is the relationship between completing the square and the quadratic formula?

• They are unrelated

• They are two different methods for solving linear equations

• Completing the square is a step in deriving the quadratic formula

• The quadratic formula is used to complete the square