Completing the square

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
  1. What is "COMPLETING THE SQUARE"?
?
Examples
Lessons
  1. Recognizing a Polynomial that Can Be Written as a Perfect Square
    Convert the following expressions into perfect squares, if possible:
    1. x2+6x+32{x^2} + 6x + {3^2} =
      x26x+(3)2{x^2} - 6x + {\left( { - 3} \right)^2} =
    2. 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.
    1. x2+10x+  {x^2} + 10x + \;_____ =
    2. x22x+  {x^2} - 2x + \;_____ =
    3. 2x2+12x+  2{x^2} + 12x + \;_____ =
    4. 3x2+60x+   - 3{x^2} + 60x + \;_____ =
    5. 25x28x+  \frac{2}{5}{x^2} - 8x + \;_____ =
Topic Notes
?
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