Completing the Square Techniques

The video tutorial explains how to solve a quadratic equation by completing the square. It begins with setting up the problem and identifying that the equation cannot be factored traditionally. The teacher then demonstrates how to create a perfect square trinomial by moving the constant to the other side and finding the appropriate value to add. The process involves using inverse operations to solve for x, resulting in two solutions expressed in terms of square roots. The tutorial emphasizes leaving the answer in exact form rather than decimals.

What is the first step in solving the quadratic equation x^2 - 4x - 13 = 0?

• Factor the equation

• Use the quadratic formula

• Complete the square

• Move the constant to the other side

Why can't the equation x^2 - 4x - 13 = 0 be factored using normal methods?

• It is a linear equation

• It does not have integer factors

• It is already in factored form

• It has no real roots

What is the purpose of moving the constant to the other side of the equation?

• To solve for x directly

• To simplify the equation

• To factor the equation

• To create a perfect square trinomial

What is the equation after moving the constant to the other side?

• x^2 - 4x = 13

• x^2 - 4x = 0

• x^2 - 4x = 4

• x^2 - 4x = -13

How do you find the value needed to complete the square?

• Multiply b by 2 and square it

• Divide b by 2 and square it

• Add b to the constant

• Subtract b from the constant

What must you do to both sides of the equation after adding a value to complete the square?

• Divide by the same value

• Add the same value

• Multiply by the same value

• Subtract the same value

What is the value of c that completes the square for x^2 - 4x?

• 16

• 8

• 4

• 2

What is the equation after adding the value to complete the square?

• x^2 - 4x + 4 = 13

• x^2 - 4x + 4 = 17

• x^2 - 4x + 4 = 0

• x^2 - 4x + 4 = 9

What is the significance of the constant 4 in completing the square?

• It is the solution to the equation

• It creates a perfect square trinomial

• It factors the equation

• It eliminates the constant

What is the next step after writing the equation as a perfect square?

• Solve for x using inverse operations

• Use the quadratic formula

• Factor the equation

• Add the constant back