Completing the Square Concepts

The video tutorial from MooMooMath explains how to solve quadratic equations using the completing the square method. It begins with a basic introduction and then provides a detailed walkthrough of solving a quadratic equation without a leading coefficient. The tutorial continues with a more complex example involving a leading coefficient, demonstrating how to adjust the equation to complete the square. The video concludes with solving the equation and finding the roots.

What is the first step in completing the square for the equation x^2 - 4x + 35 = 35?

• Add 9 to both sides

• Factor the equation

• Take the square root of both sides

• Move the constant to the other side

How do you create a perfect square from the equation x^2 - 6x?

• Add 6 to both sides

• Add 9 to both sides

• Multiply by 2

• Subtract 6 from both sides

What is the result of factoring x^2 - 6x + 9?

• (x - 6)(x - 6)

• (x + 3)(x + 3)

• (x - 3)(x - 3)

• (x + 6)(x + 6)

After taking the square root of both sides, what must you remember to include?

• No roots are needed

• Both positive and negative roots

• Only the negative root

• Only the positive root

What is the solution for x in the equation x = -3 ± 2√11?

• x = -3 ± √11

• x = 3 ± √11

• x = 3 ± 2√11

• x = -3 ± 2√11

What should you do if the equation has a leading coefficient other than 1?

• Subtract the coefficient from both sides

• Multiply all terms by the coefficient

• Divide all terms by the coefficient

• Add the coefficient to both sides

In the equation 2x^2 - 12x = -14, what is the first step to simplify it?

• Subtract 12 from both sides

• Multiply by 2

• Divide by 2

• Add 14 to both sides

What is the result of factoring x^2 - 6x + 9 after dividing by 2?

• (x - 6)^2

• (x + 3)^2

• (x - 3)^2

• (x + 6)^2

What is the final solution for x in the equation x - 3 = ±2?

• x = 3 ± 2

• x = -3 ± 2

• x = 3 ± √2

• x = -3 ± √2

What is the key takeaway from completing the square?

• Always add the same number to both sides

• Always divide by the same number on both sides

• Always subtract the same number from both sides

• Always multiply by the same number on both sides