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Completing the square (visual explanation)

The method of completing the square can be looked upon as a method which visualizes
a quadratic equation as an incomplete square, and in the process of completing
that square, you are able to solve the quadratic equation. In the following example,
the quadratic equation x2 + 2x - 3 = 0 is visualized as an incomplete
square. In the process of completing the square, the quadratic equation is factored
to a simple form, which can be easily solved for 'x'.






In the above example, we illustrated a part of a quadratic equation visually, and
in the attempt of completing the square, it was factored to the form (x + a)2.
Once the equation is factored to this form, it is extremely easy to solve it by
taking the square root of both sides of the quadratic equation. By applying the
Zero Product Rule to the last equation obtaine above, we obtain:
  • Either x = +2 - 1 = 1
  • Or x = -2 - 1 = -3
Hence the roots of the quadratic equation x2 + 2x - 3 = 0 are calculated
by the method of completing the square as 1 and -3.