Solving Quadratic Equations by Completing the Square

The video tutorial explains how to solve quadratic equations by completing the square. It begins with a simple example, x^2 + 4x = 5, demonstrating the process of completing the square and solving for x. The tutorial then progresses to more complex examples, such as 2x^2 - 12x - 7 = 0 and 3x^2 - 5x = 10, illustrating the steps of factoring, completing the square, and solving the equations. The video emphasizes the importance of maintaining balance by performing the same operations on both sides of the equation.

What is the first step in completing the square for the equation x^2 + 4x = 5?

• Multiply both sides by 2

• Subtract 4 from both sides

• Take half of the coefficient of x and square it

• Add 4 to both sides

After completing the square for x^2 + 4x = 5, what is the resulting equation before solving for x?

• (x - 4)^2 = 5

• (x + 4)^2 = 5

• (x - 2)^2 = 9

• (x + 2)^2 = 9

What are the solutions for x in the equation x^2 + 4x = 5 after completing the square?

• x = 2 and x = -2

• x = 5 and x = -1

• x = 1 and x = -5

• x = 3 and x = -3

In the equation 2x^2 - 12x - 7 = 0, what is the first step to solve by completing the square?

• Add 7 to both sides

• Subtract 7 from both sides

• Divide by 2

• Multiply by 2

When completing the square for 2x^2 - 12x = 7, what value is added to both sides after factoring out the 2?

• 9

• 18

• 36

• 6

What is the final form of the equation 2x^2 - 12x - 7 = 0 after completing the square and before solving for x?

• (x - 3)^2 = 25/2

• (x - 3)^2 = 25

• (x + 3)^2 = 25/2

• (x + 3)^2 = 25

What are the solutions for x in the equation 2x^2 - 12x - 7 = 0 after completing the square?

• x = 3 ± 5√2/2

• x = 3 ± 5/√2

• x = 3 ± 5/2

• x = 3 ± 5√2

In the equation 3x^2 - 5x = 10, what is the first step to solve by completing the square?

• Subtract 5 from both sides

• Divide by 3

• Factor out 3

• Add 5 to both sides

What is half of the coefficient of x in the equation 3x^2 - 5x = 10 after factoring out the 3?

• 5/3

• 5/6

• 5/12

• 5/2

What is the final form of the equation 3x^2 - 5x = 10 after completing the square and before solving for x?

• (x - 5/6)^2 = 145/12

• (x + 5/6)^2 = 145/12

• (x + 5/6)^2 = 145/36

• (x - 5/6)^2 = 145/36