document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=440412>Question 440412</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular sheet of paper has an area of 204in. squared. Its dimensions are (x+4) by (x+9). What are the dimensions of the paper.\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 #304237 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=304237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular sheet of paper has an area of 204in. squared. Its dimensions are (x+4) by (x+9). What are the dimensions of the paper.<BR>\n" );
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document.write( "since area is width times length:<BR>\n" );
document.write( "204 = (x+4)(x+9)<BR>\n" );
document.write( "FOIL the right:<BR>\n" );
document.write( "204 = x^2+9x+4x+36<BR>\n" );
document.write( "204 = x^2+13x+36<BR>\n" );
document.write( "0 = x^2+13x-170<BR>\n" );
document.write( "solve by applying the quadratic formula to get:<BR>\n" );
document.write( "x = {8.1, -21.1}<BR>\n" );
document.write( "throw out the negative solution leaving:<BR>\n" );
document.write( "x = 8.1<BR>\n" );
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document.write( "dimensions are:<BR>\n" );
document.write( "12.1 inch by 17.1 inch<BR>\n" );
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document.write( "details of quadratic follows:<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=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=1x%5E2%2B13x%2B-170+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B13x%2B-170+=+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=%2813%29%5E2-4%2A1%2A-170=849 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2813%29%5E2-4%2A1%2A-170=849\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=849 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+=+%28-13%2B-sqrt%28+849+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-13%2B-sqrt%28+849+%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-%2813%29%2Bsqrt%28+849+%29%29%2F2%5C1+=+8.06880228433347 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2813%29%2Bsqrt%28+849+%29%29%2F2%5C1+=+8.06880228433347\"   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-%2813%29-sqrt%28+849+%29%29%2F2%5C1+=+-21.0688022843335 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2813%29-sqrt%28+849+%29%29%2F2%5C1+=+-21.0688022843335\"   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=1x%5E2%2B13x%2B-170 ALIGN=MIDDLE  ALT=\"1x%5E2%2B13x%2B-170\"   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=1x%5E2%2B13x%2B-170+=+1%28x-8.06880228433347%29%2A%28x--21.0688022843335%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B13x%2B-170+=+1%28x-8.06880228433347%29%2A%28x--21.0688022843335%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 8.06880228433347, -21.0688022843335.\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+1%2Ax%5E2%2B13%2Ax%2B-170+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B13%2Ax%2B-170+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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