Why is completing the square called completing the square?

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#1
Report Thread starter 9 years ago
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Hi

I know how to use the 'complete the square' method to solve quadratics. Very familiar with the process.

But I'd like to know at what stage in workings are we 'completing' a square - just interested to know why the process is called that.

Thanks.
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BabyMaths
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x^2+4x is not a 'square'.

x^2+4x+4-4 completes the square.

leading to..

(x+2)^2-4
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bananarama2
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Notnek
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Good question - I wondered the same thing at school and my teacher couldn't explain it to me.

e.g. x^2+6x+3=0


x^2+6x+3 is not a perfect square. x^2+6x is not a perfect square as well but it does make up three of the four quadrants of a square, x^2, 3x and 3x, where the square is (x+3)^2.* To fill in the gap and "complete the square" we add a 9 to both sides to get


x^2+6x+9+3=9 \implies (x+3)^2-6=0

*If this part is confusing to you, try drawing a square with length x+3.
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#5
Report Thread starter 9 years ago
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Thanks to three of you for helpful answers - appreciate the time taken.

ugk4life - no thanks at all for your silly post.
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