Quadratic Equation: Completing the Square

The video tutorial explains how to solve a quadratic equation by completing the square. It begins by transforming the equation into a specific form and then dividing by the coefficient of x squared. The process continues by creating a perfect square trinomial, factoring it, and solving for x. The tutorial concludes by finding the solutions and reflecting on the method used, emphasizing that the solutions are real and rational.

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

• Subtract a constant from both sides

• Divide both sides by a constant

• Multiply both sides by a constant

• Add a constant to both sides

If the coefficient of x squared is not 1, what should you do?

• Divide both sides by it

• Add it to both sides

• Subtract it from both sides

• Multiply both sides by it

What is added to both sides to create a perfect square trinomial?

• The square of the coefficient of x squared

• The square of the constant term

• The square of half the coefficient of x

• The square of the coefficient of x

What is the purpose of factoring the left side of the equation?

• To eliminate the constant term

• To create a perfect square trinomial

• To find the roots of the equation

• To simplify the equation

What operation is performed to solve for x after factoring?

• Multiplication

• Square rooting

• Subtraction

• Addition

What is the result of square rooting both sides of the equation?

• A single solution for x

• An infinite number of solutions for x

• No solution for x

• Two possible solutions for x

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

• Dividing both sides by a constant

• Multiplying both sides by a constant

• Subtracting a constant from both sides

• Adding a constant to both sides

What are the solutions to the equation after completing the square?

• x = -1 and x = 2

• x = 1/2 and x = 3/2

• x = 0 and x = 1

• x = -5/2 and x = -1

Why are the solutions to the quadratic equation real and rational?

• Because the equation was solved by substitution

• Because the equation was solved by factoring

• Because the equation was solved by completing the square

• Because the equation was solved by graphing

What method could have been used instead of completing the square?

• Elimination

• Factoring

• Substitution

• Graphing