Completing the Square with Coefficient Step by Step

This video tutorial provides a detailed explanation of completing the square for quadratic equations with coefficients and fractions. It covers the process of grouping terms, factoring out coefficients, finding the value of C, and simplifying the expression. The tutorial aims to make the steps clear and ingrained for solving complex problems involving completing the square.

Why is completing the square considered an important process in solving quadratic equations?

• It eliminates the need for any calculations.

• It is the fastest method to solve any equation.

• It helps in transforming a quadratic equation into a perfect square trinomial.

• It is the only method to solve quadratic equations.

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

• Factoring out the constant term.

• Simplifying the equation.

• Grouping the quadratic and linear terms.

• Finding the value of C.

When factoring out the coefficient of the quadratic term, what should you do if it does not divide evenly into the linear term?

• Add the coefficient to the constant term.

• Multiply the entire equation by the coefficient.

• Factor it out as a fraction.

• Ignore the coefficient.

How do you determine the value of C when completing the square?

• Divide the middle term by 2 and square it.

• Add the middle term to the constant term.

• Multiply the middle term by 2 and square it.

• Subtract the middle term from the constant term.

What must you ensure when adding the value of C to the equation?

• Add and subtract it on the same side to keep the equation balanced.

• Multiply it by the coefficient of the quadratic term.

• Add it only to one side of the equation.

• Ignore it if it is a fraction.

How can you recognize a perfect square trinomial when dealing with fractions?

• By checking if the trinomial can be factored into a binomial squared.

• By adding the fractions together.

• By ensuring all terms are whole numbers.

• By multiplying all terms by the same fraction.

What is the final step in completing the square when dealing with fractions?

• Adding all terms together.

• Simplifying the expression by finding common denominators.

• Multiplying the entire equation by a constant.

• Subtracting the fractions from each other.