Quadratic Equation: Completing the Square

This video tutorial explains how to solve a quadratic equation by completing the square. It assumes prior knowledge of the basic steps involved. The process includes moving the constant term, making the leading coefficient one, creating a perfect square trinomial, and factoring it to solve for x. The tutorial provides detailed steps and calculations, emphasizing the importance of maintaining equality and using a common denominator. The final solution is presented in two forms, highlighting the presence of two real irrational solutions.

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

• Move the constant term to the right side of the equation.

• Add a constant to both sides.

• Multiply all terms by the leading coefficient.

• Take the square root of both sides.

Why do we divide all terms by the leading coefficient when completing the square?

• To simplify the constant on the right side.

• To eliminate the constant term.

• To ensure the leading coefficient is 1.

• To make the equation easier to solve.

How do you determine the constant needed to complete the square?

• Add the coefficient of x to the constant term.

• Multiply the coefficient of x by 2 and square it.

• Divide the coefficient of x by 2 and square it.

• Subtract the constant term from the coefficient of x.

What is the purpose of factoring the trinomial in the process of completing the square?

• To find the roots of the equation.

• To simplify the equation.

• To eliminate the x term.

• To express it as a product of binomials.

What must be done after factoring the trinomial to solve for x?

• Add the constant to both sides.

• Multiply both sides by the leading coefficient.

• Take the square root of both sides.

• Subtract the constant from both sides.

Why is it necessary to include a plus or minus sign when taking the square root of both sides?

• To account for both positive and negative roots.

• To ensure the equation is balanced.

• To simplify the equation.

• To eliminate the constant term.

What is the final form of the solution for x in this method?

• x equals a fraction with a square root.

• x equals a constant.

• x equals a binomial squared.

• x equals a trinomial.

What type of solutions are obtained when the square root of a non-perfect square is involved?

• No solutions.

• Real and irrational solutions.

• Complex solutions.

• Real and rational solutions.

How can the solution be expressed when there is a common denominator?

• As a difference of fractions.

• As a sum of fractions.

• As a product of fractions.

• As a single fraction.

What does the final solution represent in terms of the quadratic equation?

• The roots of the equation.

• The vertex of the parabola.

• The y-intercept.

• The axis of symmetry.