document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178715>Question 178715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help.<BR>\n" );
document.write( "Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133698 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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/cgi-bin/show-face.mpl?user=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=133698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?<BR>\n" );
document.write( ".<BR>\n" );
document.write( "It's important to draw a diagram of the problem.<BR>\n" );
document.write( "Once you do that, it'll be easier to \"see\" the solution.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let x = measure of one side of ths square that is being cut from each corner<BR>\n" );
document.write( "then area of the base would be<BR>\n" );
document.write( "(11-2x)(14-2x) = 80<BR>\n" );
document.write( "FOIL the left:<BR>\n" );
document.write( "154 - 22x - 28x + 4x^2 = 80<BR>\n" );
document.write( "154 - 50x + 4x^2 = 80<BR>\n" );
document.write( "Rearranging...<BR>\n" );
document.write( "4x^2 - 50x + 154 = 80<BR>\n" );
document.write( "4x^2 - 50x + 74 = 0<BR>\n" );
document.write( "2x^2 - 25x + 37 = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since we can't factor you must apply the quadratic equation.  Doing so yields:<BR>\n" );
document.write( "x = {10.785, 1.715}<BR>\n" );
document.write( "As you can see, there are two possible solutions -- but, the one that makes the most sense would be 1.715 inches the other will make an awfully funny shape box.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Below are the details of the quadratic:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=quadratic.solver>SOLVE quadratic equation with variable</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" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
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" );
document.write( "    <BR>\n" );
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+=+2%28x-10.7845892868043%29%2A%28x-1.71541071319574%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-25x%2B37+=+2%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" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );