Solving Quadratic Equations by Completing the Square

This video tutorial teaches how to solve quadratic equations by completing the square. It begins with an introduction to the method, explaining the process of transforming a non-perfect square trinomial into a perfect square trinomial. The tutorial highlights common mistakes, such as handling leading coefficients greater than one, and provides a detailed example to illustrate the correct steps. By the end, viewers will understand how to apply the method to solve quadratic equations effectively.

What is the first step in completing the square for the equation X^2 + 4X - 8 = 0?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 4 from both sides

• Add 8 to both sides

When completing the square, why is it important to have a leading coefficient of one?

• It eliminates the need for a constant term

• It simplifies the factoring process

• It makes the equation linear

• It ensures the equation is quadratic

What common mistake might occur when the leading coefficient is not one?

• Ignoring the constant term

• Multiplying the equation by zero

• Adding the wrong constant to both sides

• Forgetting to factor out the coefficient

In the example X^2 + 4X - 8 = 0, what is the value added to both sides to complete the square?

• 2

• 4

• 12

• 8

After completing the square and taking the square root, what are the possible solutions for X in the equation X^2 + 4X - 8 = 0?

• X = 2 + sqrt(12) and X = 2 - sqrt(12)

• X = -2 + sqrt(8) and X = -2 - sqrt(8)

• X = -2 + sqrt(12) and X = -2 - sqrt(12)

• X = 2 + sqrt(8) and X = 2 - sqrt(8)