Completing the square

Completing the square

Lessons

perfect squares:
  • (x+a)2=x2+2ax+a2{\left( {x + a} \right)^2} = {x^2} + 2ax + {a^2}
  • (xa)2=x22ax+a2{\left( {x - a} \right)^2} = {x^2} - 2ax + {a^2}
  • completing the square: adding a constant to a quadratic expression to make it a perfect square
    • Introduction
      What is "COMPLETING THE SQUARE"?

    • 1.
      Recognizing a Polynomial that Can Be Written as a Perfect Square
      Convert the following expressions into perfect squares, if possible:
      a)
      x2+6x+32{x^2} + 6x + {3^2} =
      x26x+(3)2{x^2} - 6x + {\left( { - 3} \right)^2} =

      b)
      x2+20x+100{x^2} + 20x + 100 =
      x220x+100{x^2} - 20x + 100 =
      x220x100{x^2} - 20x - 100 =


    • 2.
      Completing the Square
      Add a constant to each quadratic expression to make it a perfect square.
      a)
      x2+10x+{x^2} + 10x + \;_____ =

      b)
      x22x+{x^2} - 2x + \;_____ =

      c)
      2x2+12x+2{x^2} + 12x + \;_____ =

      d)
      3x2+60x+ - 3{x^2} + 60x + \;_____ =

      e)
      25x28x+\frac{2}{5}{x^2} - 8x + \;_____ =