document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176011>Question 176011</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> thomas is going to make an open top box by cutting equal squares from the four corners on an 11 inch by 14 inch sheet of cardboard and folding up the sides. if the area of the base is to be 80 sqare inches then what size should be cut from each corner?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131122 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=131122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = side of the cut-out squares.\r<BR>\n" );
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document.write( "The length of the base is: 14 - 2x inches.<BR>\n" );
document.write( "The width of the base is: 11 - 2x inches.\r<BR>\n" );
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document.write( "The area of the base is 80 in².\r<BR>\n" );
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document.write( "There is our equation:  (14 - 2x)(11 - 2x)  =  80\r<BR>\n" );
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document.write( "  and we have the quadratic:  2x² - 25x + 37  =  0\r<BR>\n" );
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document.write( "The Quadratic Formula gives us:  x  =  ¼(25 ± &#8730;239)\r<BR>\n" );
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document.write( "The smaller root is the answer:  x = ¼(25 - &#8730;329) &#8776; 1.7154 inches\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-25x%2B37+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-25x%2B37+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
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document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-25%29%5E2-4%2A2%2A37=329 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-25%29%5E2-4%2A2%2A37=329\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=329 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--25%2B-sqrt%28+329+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--25%2B-sqrt%28+329+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-25%29%2Bsqrt%28+329+%29%29%2F2%5C2+=+10.7845892868043 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-25%29%2Bsqrt%28+329+%29%29%2F2%5C2+=+10.7845892868043\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-25%29-sqrt%28+329+%29%29%2F2%5C2+=+1.71541071319574 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-25%29-sqrt%28+329+%29%29%2F2%5C2+=+1.71541071319574\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-25x%2B37 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-25x%2B37\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-25x%2B37+=+%28x-10.7845892868043%29%2A%28x-1.71541071319574%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-25x%2B37+=+%28x-10.7845892868043%29%2A%28x-1.71541071319574%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 10.7845892868043, 1.71541071319574.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-25%2Ax%2B37+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-25%2Ax%2B37+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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