Completing the square to solve a quadratic with irrational solutions

The video tutorial guides students through the process of completing the square in a quadratic equation. It begins with an overview of the steps, emphasizing the importance of grouping terms and factoring to create a perfect square trinomial. The instructor explains how to simplify fractions and solve the equation, addressing common errors and ensuring clarity. The tutorial concludes with the final solution, highlighting the importance of understanding each step in the process.

What is the first step in completing the square?

• Group the first two terms

• Convert to a decimal

• Factor out the greatest common factor

• Add a constant to both sides

Why is it important to ensure 'a' equals 1 when completing the square?

• To simplify the equation

• To factor out the variable

• To create a perfect square trinomial

• To eliminate fractions

What should you do with fractions when simplifying an expression?

• Convert them to decimals

• Simplify them

• Ignore them

• Multiply them by 2

How do you handle subtracting a fraction from a whole number?

• Add the fraction to the whole number

• Ignore the fraction

• Convert the whole number to a fraction with a common denominator

• Multiply the fraction by the whole number

What is the next step after isolating the squared term in the equation?

• Add a constant to both sides

• Take the square root of both sides

• Multiply both sides by 2

• Subtract a constant from both sides

What must you remember to include when taking the square root of both sides?

• A constant

• A fraction

• Plus or minus

• A variable

What is the final form of the solution after completing the square?

• X = 5 ± sqrt 15

• X = 5 halves ± sqrt 15 / 2

• X = 5 halves ± sqrt 15

• X = 5 ± sqrt 15 / 2