What does completing the square mean?

1 Answer
Sep 16, 2014

Completing the square is a method that represents a quadratic equation as a combination of quadrilateral used to form a square.

The basis of this method is to discover a special value that when added to both sides of the quadratic that will create a perfect square trinomial.

That special value is found by evaluation the expression #(b/2)^2# where #b# is found in #ax^2+bx+c=0#. Also in this explanation I assume that #a# has a value of #1#.

#ax^2+bx+(b/2)^2=(b/2)^2-c#

#(ax+b/2)^2=(b/2)^2-c#

#sqrt((ax+b/2)^2)=+-sqrt((b/2)^2-c)#

#ax+b/2=+-sqrt((b/2)^2-c)#

#ax=+-sqrt((b/2)^2-c)-b/2#

A quadratic that is a perfect square is very easy to solve.

Please take a look at the video to see an example of completing the square visually.

Completing the Square