Question

What does completing the square mean?

Answer 1

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