How to solve a quadratic equation by completing the square when a is not one

The video tutorial explains how to solve quadratic equations by completing the square, especially when the leading coefficient is not 1. The instructor guides through the process of factoring out the coefficient to make it 1, completing the square, and solving the equation. The tutorial concludes with the realization that the equation has no real solutions due to a negative square root.

Why is it important to set the equation equal to zero before solving?

• To simplify the equation

• To ensure the equation is balanced

• To apply the quadratic formula

• To make factoring easier

What adjustment is necessary when the coefficient of the quadratic term is not one?

• Multiply the equation by zero

• Factor out the coefficient

• Subtract the coefficient from both sides

• Add a constant to both sides

What is the main goal of factoring out the coefficient of the quadratic term?

• To eliminate the constant term

• To make the equation easier to solve

• To ensure the quadratic term has a coefficient of one

• To simplify the linear term

What is the first step in completing the square?

• Multiply the linear coefficient by two

• Divide the linear coefficient by two and square it

• Add the linear coefficient to the constant term

• Subtract the linear coefficient from the quadratic term

When completing the square, what must be done after adding the squared term inside the parentheses?

• Subtract the squared term from the constant

• Multiply the squared term by the original coefficient

• Add the squared term to the other side of the equation

• Divide the squared term by the linear coefficient

What is the result when the square root of a negative number is encountered?

• No real solutions

• A zero solution

• A complex solution

• A positive solution

If the square root of a negative number is not involved, what would the solution look like?

• x equals zero

• x equals a negative number

• x equals plus or minus the square root of a positive number minus one

• x equals the square root of a positive number