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The Hindu method for completing the square

Published online by Cambridge University Press:  01 August 2016

Dave L. Renfro
Dave L. Renfro*
Affiliation:
ACT Inc., Iowa City IA 52243-0168, USA, e-mail dave.renfro@act.org
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In a September 2005 note in The Mathematics Teacher, Gordon [1] gave a variation on the method of completing the square that fraction-phobic students are likely to find easier, along with the comment: ‘This variation is so obvious it must have been discovered many times over, but I have never seen it in print and thought it would be useful to disseminate it more widely.’ The method Gordon [1] gave is to multiply by 4a, and then add b2 , to both sides of ax2 + bx = −c to produce 4a2x2 + 4abx + b2 = b2 −4ac. The left side of this last equation can be factorised as (2ax + b)2, and now we have a pure quadratic whose solution is straightforward.

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Articles
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The Mathematical Gazette , Volume 91 , Issue 521 , July 2007, pp. 198 - 201
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Copyright © The Mathematical Association 2007

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