document.write( "Question 1172812: Suppose you have 20 inches by 16 inches cardboard. You need to cut
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Algebra.Com's Answer #797925 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let x be the size of the square to cut at each corner (in inches).\r\n" );
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document.write( "Then the dimensions of the base of the box will be  (20-2x) inches and (16-2x) inches;\r\n" );
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document.write( "the height of the box will be x inches.\r\n" );
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document.write( "So, the volume of the box is  x*(20-2x)*(16-2x) cubic inches.\r\n" );
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document.write( "It gives you an equation\r\n" );
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document.write( "     x*(20-2x)*(16-2x) = 384.\r\n" );
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document.write( "Simplify by dividing both sides by 4\r\n" );
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document.write( "    x*(10-x)*(8-x) = 96.\r\n" );
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document.write( "It is a cubic equation.\r\n" );
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document.write( "You can solve it graphically, or by trial and error method, or using the Rational root test.\r\n" );
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document.write( "From the plot below, you can see that the roots of the last equation are x= 2, x= 4  and  x= 12.  \r\n" );
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document.write( "It is clear that the roots x= 2 and x= 4 are the solutions to the problem, while the root x= 12 is not.   \r\n" );
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document.write( "Having it, you may compute the possible areas of the cut squares.\r\n" );
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document.write( "            Plot y = x*(10-x)*(8-x) - 96\r\n" );
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