document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118426>Question 118426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An open box is to be made from a 10 cm by 20 cm rectangular piece of cardboard by cutting a square from each corner and folding up the sides.  The area of the bottom of the box is 96 cm squared.  What is the length of the sides of the squares that are cut from the corners?\r<BR>\n" );
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document.write( "I really need help solving this algebraically. If you could help that would be amazing!   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86551 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you draw a picture, you can see that the dimensions of the bottom of the box are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20-2x ALIGN=MIDDLE  ALT=\"20-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-2x ALIGN=MIDDLE  ALT=\"10-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the area of the bottom is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%2820-2x%29%2810-2x%29 ALIGN=MIDDLE  ALT=\"A=%2820-2x%29%2810-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96=%2820-2x%29%2810-2x%29 ALIGN=MIDDLE  ALT=\"96=%2820-2x%29%2810-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now plug in the given area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=96 ALIGN=MIDDLE  ALT=\"A=96\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96=200-60x%2B4x%5E2 ALIGN=MIDDLE  ALT=\"96=200-60x%2B4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=200-60x%2B4x%5E2-96 ALIGN=MIDDLE  ALT=\"0=200-60x%2B4x%5E2-96\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 96 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=104-60x%2B4x%5E2 ALIGN=MIDDLE  ALT=\"0=104-60x%2B4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4x%5E2-60x%2B104 ALIGN=MIDDLE  ALT=\"0=4x%5E2-60x%2B104\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%5E2-60%2Ax%2B104=0 ALIGN=MIDDLE  ALT=\"4%2Ax%5E2-60%2Ax%2B104=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-60 ALIGN=MIDDLE  ALT=\"b=-60\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=104 ALIGN=MIDDLE  ALT=\"c=104\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--60+%2B-+sqrt%28+%28-60%29%5E2-4%2A4%2A104+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28--60+%2B-+sqrt%28+%28-60%29%5E2-4%2A4%2A104+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=4, b=-60, and c=104\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860+%2B-+sqrt%28+%28-60%29%5E2-4%2A4%2A104+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B-+sqrt%28+%28-60%29%5E2-4%2A4%2A104+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -60 to get 60\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860+%2B-+sqrt%28+3600-4%2A4%2A104+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B-+sqrt%28+3600-4%2A4%2A104+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -60 to get 3600  (note: remember when you square -60, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-60%29%5E2=-60%2A-60=3600 ALIGN=MIDDLE  ALT=\"%28-60%29%5E2=-60%2A-60=3600\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860+%2B-+sqrt%28+3600%2B-1664+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B-+sqrt%28+3600%2B-1664+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A104%2A4 ALIGN=MIDDLE  ALT=\"-4%2A104%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1664 ALIGN=MIDDLE  ALT=\"-1664\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860+%2B-+sqrt%28+1936+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B-+sqrt%28+1936+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860+%2B-+44%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B-+44%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860+%2B-+44%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B-+44%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 4 to get 8\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860+%2B+44%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%2860+%2B+44%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860+-+44%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%2860+-+44%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets look at the first part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=104%2F8 ALIGN=MIDDLE  ALT=\"x=104%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13 ALIGN=MIDDLE  ALT=\"x=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So one answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13 ALIGN=MIDDLE  ALT=\"x=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets look at the second part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2860+-+44%29%2F8 ALIGN=MIDDLE  ALT=\"x=%2860+-+44%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=16%2F8 ALIGN=MIDDLE  ALT=\"x=16%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So another answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13 ALIGN=MIDDLE  ALT=\"x=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, since 13 is greater than 10, the solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13 ALIGN=MIDDLE  ALT=\"x=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not possible since the square cutout cannot have a longer length than one of the sides.\r<BR>\n" );
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document.write( "So our only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "------------\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Remember, the area is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%2820-2x%29%2810-2x%29 ALIGN=MIDDLE  ALT=\"A=%2820-2x%29%2810-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96=%2820-2%282%29%29%2810-2%282%29%29 ALIGN=MIDDLE  ALT=\"96=%2820-2%282%29%29%2810-2%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the given area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=96 ALIGN=MIDDLE  ALT=\"A=96\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96=%2820-4%29%2810-4%29 ALIGN=MIDDLE  ALT=\"96=%2820-4%29%2810-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96=%2816%29%286%29 ALIGN=MIDDLE  ALT=\"96=%2816%29%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96=96 ALIGN=MIDDLE  ALT=\"96=96\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply. Since the two sides of the equation are equal, this verifies our answer. </SPAN>\n" );
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