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Algebra-Completing the Square

Completing the square song. Actually it is more like a short jingle. However, this little jingle can help you remember the steps for completing a square when solving a quadratic equation. The video works several example problems in which completing the square is used to solve the equation. If you have been really confused about "completing the square" this jingle and video will help. I have taught hundreds of students how to master this method of solving quadratic equations.

Before you get started with completing the square, remember this jingle. Just sing it to your favorite song.
We half it, we square it, and we add it to both sides.
We half it, we square it, and we add it to both sides.

Take the quadratic equation,
X^2 -8x -4 =0

  • Step 1 involves taking b term (8x in the example above) and you half it, square it, and add it to both sides. 
  • Next you factor the left side which creates a perfect square. 
  • You then take the square root of both sides of the equation.
  •  In the example above you are left with x-4 = + - √20
  • Isolate the x by adding 4 to both sides.
  • Finally, we just add our answer, and simplify our radical. You will have two solutions. That is how you complete the square using our jingle.
  • Completing the square sounds really complicated on paper, but when you watch the problems being worked out it will seem much easier.






4 resources to help with "Completing the Square"

Completing the Square/Regents test prep  This resource gives step by step directions for how to complete the square. Regents test prep is created by a school district and I find their resources helpful.

Video Complete the Square/Math Meeting  I watched many videos covering this topic and I felt this video was the best.

Complete the square calculator   Just type in the equation and this calculator will solve using the quadratic equation. Helpful for checking your homework.

Complete the Square Worksheets with answers  Use these worksheets with your class or quiz yourself.