Completing the Square Quiz

What is the first step in solving a quadratic equation by completing the square when the coefficient of x squared is not one?

• Add a constant to both sides

• Collect all variable terms on one side

• Multiply both sides by the coefficient

• Subtract the constant from both sides

Why do we divide by the coefficient of x squared in the process of completing the square?

• To make the equation simpler

• To eliminate fractions

• To balance the equation

• To ensure the coefficient of x squared is one

In the example problem, what number is added to both sides to complete the square?

• 4

• 16

• 2

• 8

What is the challenging part of solving the example problem with fractions?

• Multiplying by the coefficient

• Finding the square root

• Adding fractions to both sides

• Dividing by zero

What is the result of adding 1/3 and 1/9 in the example problem?

• 1/3

• 4/9

• 1/9

• 2/3

In the final example, what is the result of completing the square when the right side is -7?

• x + 2 = ±i7

• x + 2 = ±√-7

• x + 2 = ±i√7

• x + 2 = ±√7

What is the imaginary unit 'i' used for in the final example?

• To balance the equation

• To handle the square root of a negative number

• To simplify the equation

• To represent a negative number

What is the final form of the solution in the last example?

• 2 ± i√7

• -2 ± √7

• 2 ± √7

• -2 ± i√7

What should you do after completing the square and before solving for x?

• Multiply both sides by the coefficient

• Square root both sides

• Subtract the constant from both sides

• Add the constant to both sides

What is the importance of writing two equations after taking the square root?

• To simplify the equation

• To account for both positive and negative solutions

• To check for errors

• To balance the equation