document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=949113>Question 949113</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the length of a rectangle is 13 centimeters less than six times its width. it's area is 15 square centimeters. find the dimensions of the rectangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579404 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=579404\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> W=width; L=length=6W-13 cm;A=L*W=15 sq cm<BR>\n" );
document.write( "A=L*W<BR>\n" );
document.write( "15 sq cm=L*W Substitute for L.<BR>\n" );
document.write( "15 sq cm=(6W-13)(W)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15+sq+cm=6W%5E2-13W ALIGN=MIDDLE  ALT=\"15+sq+cm=6W%5E2-13W\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 15 sq cm from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=6W%5E2-13W-15+sq+cm ALIGN=MIDDLE  ALT=\"0=6W%5E2-13W-15+sq+cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=aW%5E2%2BbW%2Bc=0 ALIGN=MIDDLE  ALT=\"aW%5E2%2BbW%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6W%5E2%2B-13W%2B-15+=+0 ALIGN=MIDDLE  ALT=\"6W%5E2%2B-13W%2B-15+=+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=W%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"W%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=%28-13%29%5E2-4%2A6%2A-15=529 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-13%29%5E2-4%2A6%2A-15=529\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=529 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+529+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--13%2B-sqrt%28+529+%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=W%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+529+%29%29%2F2%5C6+=+3 ALIGN=MIDDLE  ALT=\"W%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+529+%29%29%2F2%5C6+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5B2%5D+=+%28-%28-13%29-sqrt%28+529+%29%29%2F2%5C6+=+-0.833333333333333 ALIGN=MIDDLE  ALT=\"W%5B2%5D+=+%28-%28-13%29-sqrt%28+529+%29%29%2F2%5C6+=+-0.833333333333333\"   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=6W%5E2%2B-13W%2B-15 ALIGN=MIDDLE  ALT=\"6W%5E2%2B-13W%2B-15\"   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=6W%5E2%2B-13W%2B-15+=+6%28W-3%29%2A%28W--0.833333333333333%29 ALIGN=MIDDLE  ALT=\"6W%5E2%2B-13W%2B-15+=+6%28W-3%29%2A%28W--0.833333333333333%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3, -0.833333333333333.\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+6%2Ax%5E2%2B-13%2Ax%2B-15+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-13%2Ax%2B-15+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "The answer we want is 3 ANSWER: Width is 3 cm.<BR>\n" );
document.write( "L=6W-13=6(3)-13=18-13=5 cm ANSWER: Length is 5 cm.<BR>\n" );
document.write( "CHECk:<BR>\n" );
document.write( "A=L*W<BR>\n" );
document.write( "15 sq cm=5 cm*3 cm<BR>\n" );
document.write( "15 sq cm=15 sq cm </SPAN>\n" );
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