Completing the square

• What method are we learning in this video?

  Completing the square
• How do the questions in this video differ from the last video?

  They have a coefficient of x squared
• What does the presence of 'a' in the completed square form indicate?

  It changes the completed square form structure
• What is the first step to approach a question with a coefficient of x squared?

  Factorize the first two terms
• What do we factor out when the coefficient of x squared is 3?


  3
• Why should the brackets be large when factorizing?

  To avoid confusion with inner brackets
• What do we multiply 3 by to get 3x squared plus 18x?

  x squared plus 6x
• What is the term at the end of the expression after factorization?

  Plus 20
• How do we complete the square for x squared plus 6x?

  Half the coefficient of x and square it
• What is half of the coefficient of x in x squared plus 6x?

  3
• What do we subtract when completing the square?

  Three squared, which is nine
• What is the product of 3 and negative 9?

  Negative 27
• What is the result of expanding the larger bracket after completing the square?

  3 times (x plus 3) squared
• What do we need to remember to include at the end of the process?

  The plus 20 term
• What is the final simplification of negative 27 plus 20?

  Negative 7
• What are the values of a, b, and c in the completed square form?

  a is 3, b is 3, c is negative 7
• What are the steps to complete the square for a quadratic expression with a coefficient?

  1. Factor out the coefficient of x squared.
  2. Write large brackets for clarity.
  3. Complete the square for the inner terms.
  4. Expand the larger bracket.
  5. Simplify the expression.