Talk:Completing the square

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[edit] Please verify the complete the square formula

Please verify the complete the square formula. I changed the page (before I had an account) by altering the equation to what I believe is the correct form, on 9/25/2006. Specifically, I changed the part of the equation that read: "4a^2" to "4a". I made this change while doing some calc II homework, when I realized that I was getting incorrect results with the equation that was on the page prior to my change on 9/25/2006.

After looking a bit further, I realized that the equation had previously been entered correctly, but some user (Huadpe) "corrected" the equation later to the "wrong" value: 4a^2. Although I think the equation is correct now, I'd appreciate it if a more veteran user/moderator of wikipedia with solid math knowledge could confirm the accuracy of the equation on the page, and somewhere make a public note (or cite) to that effect.

I'm a very experienced user of google and also a computer science major, yet I had difficulty finding a simple "plug-and-play" equation that would algebraically provide a completed square given the coefficients a, b, and c from ax^2 + bx + c. After much searching, I found that Wikipedia provided this equation, but it happened to have this minor error. I fear that other math students (likely at lower levels of math, or perhaps some that need refreshers like me) are likely to come to this page as their primary source in the future, and the equation will be modified to the incorrect version again. I'm not sure how wikipedia prevents this, but please put this on your "watch list".

Thanks all! Austin

Austinflorida 09:23, 21 October 2006 (UTC)

I decided to add an extra step to the equation to clarify the step where some people may be inclined to make an incorrect "correction." Without the added step, it seems that it might be easier for a user, even after a few glances, to inadvertently believe that a correction is necessary, when in fact the steps ARE algebraically correct (verified with TI Derive 6).

Austinflorida 09:50, 21 October 2006 (UTC)

[edit] Questions / Possible Additions to the Article

Does completing the square also apply to multivariate equations? The procedure is the same, say you have: x2 − 4xy + 5y2 = (x − 2y)2 + y2, This corresponds to completing the square with x, holding y constant - nothing too extraordinary. However, you can extend this process to three variables. Take for example x2 + 4xy + 8y2 + 20yz + 6z2 − 4xz = (x + 2y − 2z)2 + (2(y + 3z))2 − 34z2, (if my algebra is correct!) This is also an application of completing the square, allowing us to write a quadratic polyomial of three variables in which all terms have degree two, as the sum of three squares.

(My inspiration was a multivariate calculus problem: Create a tranformation to map the ellipsoid Failed to parse (Cannot write to or create math output directory): x^{2} + 4xy + 8y^{2} +4yz + 6z^{2} - 2xz = 9,

onto the unit sphere.)

--D Mac 04:39, 17 November 2005 (UTC)

These discussions cut to the heart of quadric surfaces.

Consider equations of the form a*x^2 + b*y^2 + c*x*y + d*x + e*y + f = 0, where a,b,c,d,e,f are constants. In other words, we are talking about a polynomial of several variables where the maximum degree is 2 (x^2, xy, etc). Equations of this form are combinations of scaling, rotation, and translation of an ellipse/hyperbola/parabola. This can be seen more rigorously with linear algebra. —Preceding unsigned comment added by 98.203.237.75 (talk) 04:16, 12 January 2008 (UTC)

Completing the square works no matter what the coefficients of the polynomial, as long as they don't contain the variable that is being 'completed'. I have modified the article to reflect this.

Michaelbusch 04:00, 24 August 2006 (UTC)

[edit] Vandalism

Last evening, an anon user blanked this page. I reverted it and warned the user. Please pay special attention to this page on your watch list to spot any future vandalism. 48v 00:10, 5 September 2006 (UTC)

[edit] Reorganization

I just did a significant reorganization of this article. I changed very little content, but added an Overview section heading for everything that was in the intro previously but for its first paragraph, moved the canonical quadratic equation to its own example, and subsectioned out and reordered the several examples (from most specific to most general). I tweaked a lot of math markup to look nicer, and changed the discourse on just manipulating a x^2 + b x + c to actually finding its roots, as this is arguably the most significant application of the topic (which I also noted).

I was considering removing some examples for space, perhaps what are now the second and fourth. But I decided to let this version stand and see what comments came first. Baccyak4H 16:38, 27 October 2006 (UTC)

[edit] Cleanup

I've done a major cleanup, taking advantage of the new and improved texvc, which can now handle the "align" environment. Along the way I polished the prose and pruned the examples. I did not touch the intro, though it needs work. --KSmrqT 08:52, 26 November 2006 (UTC)

[edit] Upload Image to Geometric Perspective

Could someone with a user account please upload the following image and place it in the Geometric Perspective section. Thanks. I believe this will add some intuitive perspective to the algebraic manipulations. http://1073741824.org/square_thumb.png —Preceding unsigned comment added by 98.203.237.75 (talk) 10:03, 8 January 2008 (UTC)