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Example:Solving Quadratic Equation (Completing Square)

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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





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 ax2 + 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 x2. For example:

(Our solved example in mathguru.com uses this concept).




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.