Quadratic Equation: Completing the Square

The video tutorial explains how to solve a quadratic equation by completing the square. It begins by isolating the constant term and preparing the equation. The process involves making the coefficient of x squared equal to one, completing the square, and maintaining equality by adding terms to both sides. The tutorial then covers factoring the trinomial and solving for x, resulting in two real irrational solutions. The video concludes with a summary of the steps and the types of solutions obtained.

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

• Multiply both sides by the coefficient of x squared

• Isolate the constant term on one side

• Add the square of the coefficient of x

• Factor the equation

Why do we divide both sides of the equation by 3 in the process of completing the square?

• To factor the equation

• To simplify the equation

• To make the coefficient of x squared equal to 1

• To eliminate the constant term

What value do we add to both sides to complete the square for the equation x^2 + (7/3)x?

• 49/36

• 7/6

• 14/3

• 1/2

What is the least common denominator used to add fractions on the right side of the equation?

• 36

• 24

• 12

• 48

What form does the left side of the equation take after factoring the perfect square trinomial?

• (x + 1/2)^2

• (x + 49/36)^2

• (x + 7/6)^2

• (x + 7/3)^2

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

• Addition

• Subtraction

• Multiplication

• Taking the square root

What is the simplified form of the denominator when solving for x?

• 3

• 6

• 36

• 12

What are the two solutions for x in the final step?

• 7/3 ± √73/3

• -7/3 ± √73/3

• -7/6 ± √73/6

• 7/6 ± √73/6

How can the solutions be expressed in a different form?

• 7 ± √73/6

• -7 ± √73/3

• -7 ± √73/6

• 7 ± √73/3

What type of solutions are obtained in this quadratic equation?

• One real and one complex solution

• Two real irrational solutions

• Two real rational solutions

• Two complex solutions