Solving Quadratic Equations by Completing the Square

The video tutorial covers solving a quadratic equation by completing the square and explains why a negative square root results in no solution. It also addresses a geometry problem involving the area of a parallelogram, demonstrating how to solve it using algebraic methods.

What is the first step taken to simplify the equation 2x^2 + 6x = -6?

• Subtract 6 from both sides

• Multiply everything by 2

• Divide everything by 2

• Add 6 to both sides

After dividing by 2, what is the next step in completing the square for the equation x^2 + 3x?

• Add 3 to both sides

• Multiply 3 by 2 and square it

• Subtract 3 from both sides

• Divide 3 by 2 and square it

What is the result of squaring 3/2?

• 9/4

• 3/4

• 6/4

• 1/4

What form does the equation take after completing the square?

• x^2 + 3x + 9/4 = -3 + 9/4

• x^2 + 3x + 9/4 = 3 + 9/4

• x^2 + 3x + 9/4 = 3 - 9/4

• x^2 + 3x + 9/4 = -3 - 9/4

Why is there no solution when taking the square root of both sides in the equation x + 3/2 = sqrt(-54)?

• Because the square root of a negative number is not real

• Because the square root of a negative number is zero

• Because the square root of a negative number is undefined

• Because the square root of a negative number is positive

What is the formula for the area of a parallelogram?

• Base + Height

• Base * Height

• Base - Height

• Base / Height

If the base of a parallelogram is 8 cm more than its height, how is the base represented in terms of height?

• Base = Height / 8

• Base = Height * 8

• Base = Height + 8

• Base = Height - 8

What is the equation set up to find the dimensions of the parallelogram with an area of 20 square centimeters?

• H - (H + 8) = 20

• H + (H + 8) = 20

• H * (H + 8) = 20

• H / (H + 8) = 20

What value is added to both sides to complete the square for the equation H^2 + 8H?

• 4

• 8

• 16

• 32

What are the dimensions of the parallelogram if the height is found to be 2 cm?

• Height = 2 cm, Base = 8 cm

• Height = 2 cm, Base = 10 cm

• Height = 2 cm, Base = 12 cm

• Height = 2 cm, Base = 14 cm