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Why is the technique of completing the square useful?

By Lee Mansfield on the 11th of June, 2012

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    Completing the square is a way of solving a quadratic equation without having to use any formulas. Sometimes it is quicker to do than using the quadratic formula, so that's why it's useful.

    Refine By Roger Toder on the 11th of June, 2012

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Use the technique of completing the square

A Quadratic equation has the general form:

ax2+bx+c=0

These can sometimes be factorised easily, in order to solve them.  Sometimes they cannot be factorised, but when that happens, they can always still be solved by the method of ‘completing the square’ to solve a quadratic formula.  This involves rewriting the equation in the form:

(x2+p)+q=0

Where p = ½b and q = c – ¼b2

 

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