Solving Quadratic Equations Concepts

This video tutorial explains how to solve quadratic equations by completing the square. It begins with moving the constant term to the right side of the equation, then adds a constant to form a perfect square trinomial. The tutorial continues by factoring the trinomial and solving the equation, ultimately finding complex solutions. The process is broken down into clear steps, with explanations of key concepts like perfect square trinomials and complex numbers.

What is the first step in solving a quadratic equation by completing the square?

• Add a constant to both sides

• Take the square root of both sides

• Move the constant term to the right side

• Factor the equation

When moving the constant term to the right side, what operation is performed?

• Addition

• Division

• Subtraction

• Multiplication

How do you determine the constant to add to form a perfect square trinomial?

• Add B to 2

• Subtract B from 2

• Divide B by 2 and square it

• Multiply B by 2

What is the value of B in the example given in the video?

• 9

• 6

• 12

• 3

What is the result of factoring the trinomial in the example?

• (x + 3)(x + 3)

• (x + 2)(x + 2)

• (x + 4)(x + 4)

• (x + 5)(x + 5)

What operation is used to solve for x after factoring the trinomial?

• Multiplication

• Subtraction

• Addition

• Taking the square root

What is the simplified form of the square root of -8?

• 4i

• i√8

• 2i√2

• 2i

What are the two solutions for x in the example?

• x = -3 ± i√3

• x = -3 ± 2i√3

• x = -3 ± 2i√2

• x = -3 ± i√2

How are the solutions described in the example?

• Rational solutions

• Complex solutions

• Imaginary solutions

• Real solutions

What is the final step to solve for x in the example?

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply both sides by 3

• Divide both sides by 3