Completing the Square Using a DiagramDate: 11/09/1999 at 00:08:15 From: Andy Ko Subject: Completing the square with diagram My question involves completing the square, but instead of the usual form of brackets and formula, I have to do it something like this: x^2 + 6x + ... +----------+-----+ | | | | | | | x^2 | 3x | | | | | | | +----------+------ | | | 3x | +----------+ I don't know how to draw a diagram for completing the square for: x^2 - 6x + ... The answer is x^2 - 6x + 9, but I can't draw the diagram. My teacher told me the only hint we get is that it overlaps. I can't seem to figure it out. Can you help? Thanks. Date: 11/09/1999 at 11:00:45 From: Doctor Rob Subject: Re: Completing the square with diagram Thanks for writing to Ask Dr. Math. Try this diagram: x o------------------o-----o | x-3 | 3 | | | | | | | |x-3 | | | | | | | | x | | | | | | o------------------o-----o | | | |3 | | o------------------o-----o x The lower right has area 3^2. The entire lower edge rectangle (small rectangle and square together making a longer rectangle) has area 3*x, and likewise the entire right edge rectangle has area 3*x. They overlap in the 3-by-3 square in the lower right corner. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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