Quadratic Equations: Completing the Square

The video tutorial explains how to solve quadratic equations by completing the square. It covers various examples, including equations with negative coefficients, negative signs in front, and leading coefficients not equal to one. The tutorial also addresses handling fractional coefficients and provides step-by-step instructions for each example, ensuring a comprehensive understanding of the method.

What is the first step in solving the equation x^2 + 12x + 32 = 0 by completing the square?

• Subtract 32 from both sides

• Add 32 to both sides

• Divide both sides by 2

• Multiply both sides by 2

When completing the square for x^2 - 8x + 10 = 0, what value is added to both sides?

• 8

• 16

• 64

• 4

What is the decimal approximation of 4 plus the square root of 6?

• 6.45

• 7.45

• 8.45

• 5.45

How do you handle a negative leading coefficient in a quadratic equation?

• Add a constant to both sides

• Subtract a constant from both sides

• Multiply or divide both sides by -1

• Square both sides

In the equation 2x^2 - 10x = -8, what is the first step to simplify the equation?

• Add 8 to both sides

• Subtract 8 from both sides

• Divide everything by 2

• Multiply everything by 2

What is the value of x in the equation x^2 - 5x = -4 after completing the square?

• x = 3 and x = 2

• x = 4 and x = 1

• x = 5 and x = 0

• x = 6 and x = -1

What is the square root of 9/4 when solving the equation x^2 - 5x = -4?

• 2/3

• 3/2

• 1/2

• 2

How do you divide a fraction by 2 when completing the square?

• Subtract 2 from the denominator

• Add 2 to the numerator

• Multiply the denominator by 2

• Divide the numerator by 2

What is the final form of the equation x^2 - 8/3x = -5/3 after completing the square?

• x - 4/3 squared = 1/9

• x + 4/3 squared = 1/9

• x - 5/3 squared = 1/9

• x + 5/3 squared = 1/9

What is the solution to the equation x^2 - 8/3x = -5/3 after completing the square?

• x = 5/3 and x = 2

• x = 4/3 and x = 1

• x = 4/3 and x = 2

• x = 5/3 and x = 1