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completing the square
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(Algorithm)
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Let us consider the expression , where and are real (or complex) numbers. Using the formula
we can write
This manipulation is called completing the square [1] in , or completing the square .
Replacing by , we also have
Here are some applications of this method:
- 1
- R. Adams, Calculus, a complete course, Addison-Wesley Publishers Ltd, 3rd ed.
- 2
- Matematik Lexikon (in Swedish), J. Thompson, T. Martinsson, Wahlström & Widstrand, 1991.
(Anyone has an English reference?)
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"completing the square" is owned by mathcam. [ full author list (2) | owner history (1) ]
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(view preamble)
Cross-references: function, integration technique, global minimum, equality, Calculus, polynomial, radius, center, information, hyperbola, ellipse, circle, equation, complex, real, expression
There are 6 references to this entry.
This is version 10 of completing the square, born on 2003-05-02, modified 2007-05-09.
Object id is 4237, canonical name is CompletingTheSquare.
Accessed 18443 times total.
Classification:
| AMS MSC: | 00A20 (General :: General and miscellaneous specific topics :: Dictionaries and other general reference works) |
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Pending Errata and Addenda
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