Mastering the Technique of Completing the Square

This video tutorial demonstrates how to solve a quadratic equation using the completing the square method. The instructor begins by setting up the equation and ensuring all x variables are on one side. The equation is then transformed to have a leading coefficient of one by dividing through by three. The process of completing the square is explained, followed by solving the equation using square roots. Finally, the solutions are found and verified, with the solution set presented as -3 and 5/3.

What is the first step in solving a quadratic equation by completing the square?

• Add the constant term to both sides

• Take the square root of both sides

• Divide the entire equation by the leading coefficient

• Isolate the x variables on one side

Why do we divide the entire equation by the leading coefficient?

• To eliminate the x variable

• To simplify the equation

• To prepare for taking the square root

• To make the leading coefficient one

What is the result of adding 15 to both sides of the equation?

• x² + 4x = 15

• 3x² + 4x = 15

• 3x² + 4x + 15 = 0

• x² + 4x + 15 = 0

After dividing by the leading coefficient, what is the new equation?

• 3x² + 4x = 5

• x² + 4/3x = 15/3

• x² + 4/3x = 5

• x² + 4x = 15

What is the coefficient of x after dividing the original equation by the leading coefficient?

• 2/3

• 4/3

• 1/3

• 3/4

How do you find the term to complete the square?

• Square the coefficient of x

• Square the constant term

• Multiply the coefficient of x by 2

• Divide the coefficient of x by 2 and square it

What do you do after finding the term to complete the square?

• Multiply both sides by it

• Divide both sides by it

• Add it to both sides

• Subtract it from both sides

What is the purpose of adding and subtracting the same term to complete the square?

• To isolate the x variable

• To simplify the equation

• To create a perfect square trinomial

• To balance the equation

How do you solve for x after completing the square?

• Multiply by the leading coefficient

• Divide by the coefficient of x

• Take the square root of both sides

• Subtract the constant term

What are the final solutions of the quadratic equation?

• x = 5/3 and x = -3

• x = 3/5 and x = 3

• x = -5/3 and x = 3

• x = -3 and x = 3/5