Explanation:
In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is
where x represents a variable, and a, b, and c, constants, with a ≠ 0. (If a = 0, the equation becomes a linear equation.)
The constants a, b, and c, are called respectively, the quadratic coefficient, the linear
coefficient and the constant term or free term. The term "quadratic" comes from quadratus, which is the Latin word for "square". Quadratic equations can
be solved by factoring, completing the square, graphing, Newton's method, and
using the quadratic formula
http://en.wikipedia.org/wiki/Quadratic_equation
In elementary
algebra, completing the square is a technique for converting a quadratic polynomial of the form
to the form
In this context, "constant" means not depending on x.
The expression inside the parenthesis is of the form (x − constant).
Thus one converts ax^{2} + b
x + c to
and one must find h and k.
Completing the square is used in solving quadratic equations.
General description
Given any quadratic of the form
it is possible to form a square that has the same first two terms:
This square differs from the original quadratic only in the value
of the constant term. Therefore, we can write
where k is a constant. This operation is known
as completing the square.
For example:
For an equation involving a non-monic
quadratic, the first step to solving them is to divide through by the
coefficient of x^{2}. For example:
(Our solved example in mathguru.com uses this concept).
http://en.wikipedia.org/wiki/Completing_the_square
The
above explanation is copied from Wikipedia, the free encyclopedia and is
remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported
License.