Completing the Square: a DiagramDate: 03/06/2002 at 05:28:21 From: Kelvon Goh Subject: Completing the Square Using a Diagram Can you use a diagram to show completing the square? Something like x^2+3x. Thanks. Date: 03/06/2002 at 09:03:44 From: Doctor Rick Subject: Re: Completing the Square Using a Diagram Hi, Kelvon. Are you talking about a diagram like this for x^2+3x? +----------------+-----+ 3/2 | (3/2)x | | | | | +----------------+-----+ | | | | | | | | | x | x^2 | 3 | | | - x | | | 2 | | | | | | | +----------------+-----+ x 3/2 I divided the 3x into two equal rectangles, 3/2 by x, and stuck them on the sides of the x-by-x square. To complete a large square, x+3/2 on a side, we need to add the little square with sides 3/2. x^2 + 2(3/2)x + (3/2)^2 = (x + 3/2)^2 Now, how can we make a figure when the coefficient of x is negative? We can work backwards - the x-by-x square is the BIG one, and we SUBTRACT two rectangles: +----------------+-----+ |3/2/////////////|XXXXX| |////////////////|XXXXX| +----------------+-----+ | |\\\\\| | |\\\\\| x | |\\\\\| |x-3/2 |\\\\\| | |\\\\\| | |\\\\\| | |\\\\\| | x-3/2 |\3/2\| +----------------+-----+ x We subtract two rectangles, 3/2 by x, from the x-by-x square. In doing so, we remove that little square with the X's TWICE; it's part of both rectangles. Therefore, we must add it back once, if we want to be left with just the (x-3/2) by (x-3/2) square: x^2 - 2(3/2)x + (3/2)^2 = (x - 3/2)^2 Is this what you're looking for? - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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