Quadratic Equations: Completing the Square

The video tutorial explains how to solve quadratic equations by completing the square. It begins by rewriting the equation in a specific form, then adds a constant to both sides to create a perfect square trinomial. The trinomial is factored into binomial factors, and the equation is solved for x, including handling imaginary numbers when necessary. The process is detailed step-by-step, with explanations of each part of the method.

Why can't the quadratic equation be factored in this case?

• There are no factors of 40 that add to 8.

• The equation is already in its simplest form.

• The equation has complex roots.

• The coefficient of x is too large.

What is the first step in rewriting the quadratic equation?

• Add 40 to both sides.

• Subtract 40 from both sides.

• Divide both sides by the coefficient of x.

• Multiply both sides by 2.

What constant is added to both sides to form a perfect square trinomial?

• 8

• 4

• 16

• 32

What is the purpose of taking the square root of both sides of the equation?

• To solve for x.

• To simplify the equation.

• To factor the equation.

• To eliminate the constant term.

What type of number is involved when the radicand is negative?

• Rational number

• Imaginary number

• Whole number

• Real number

What is the prime factorization of 24 used for in this context?

• To find the greatest common divisor.

• To determine the coefficient of x.

• To rewrite the equation in standard form.

• To simplify the square root.

What is the final step to solve for x in this equation?

• Add 4 to both sides.

• Subtract 4 from both sides.

• Multiply both sides by 2.

• Divide both sides by the coefficient of x.

What are the solutions to the quadratic equation?

• x = -4 ± 2√6

• x = 4 ± 2√6

• x = -4 ± 2√6i

• x = 4 ± 2√6i

What does the 'i' represent in the solutions?

• An integer

• An irrational number

• An imaginary unit

• An identity element

What is the significance of the perfect square factor in simplifying the square root of 24?

• It helps in factoring the equation.

• It changes the equation to a quadratic form.

• It simplifies the equation to a linear form.

• It allows the square root to be simplified.