GR9 Q1-L5

• Expressing square of trinomials as a square of binomials

  1. Form the x^2 + bx expression

  2. Add the square of half the coefficient of x

  3. This gives the perfect square trinomial

  4. Express the perfect square trinomial as a square of binomial
• Solving quadratic equation by completing the square

  1. Isolate the x^2 + bx expression on one side

  2. Add the square of half the coefficient of x to both sides

  3. This gives a perfect square trinomial on the left side

  4. Express the perfect square trinomial as a square of binomial

  5. Extract the square root to solve the equation
• Solving quadratic equations by completing the square

  • x^2 + 10x = 3
  • x^2 - 3x = 1
  • 2x^2 - 3x - 9 = 0
• Completing the square involves adding the square of half the coefficient of the linear term to both sides of the equation
• Expressing the perfect square trinomial as a square of binomial allows the equation to be solved by extracting the square root
• The value of x is found by solving the resulting equations after completing the square