document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=828010>Question 828010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve using quadratic formula.<BR>\n" );
document.write( "The diagonal of a rectangle is 15m long and one side is 2m longer than the other. Find the dimensions of the rectangle. <BR>\n" );
document.write( "Please HELP </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #498971 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=498971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The diagonal of a rectangle is 15m long and one side is 2m longer than the other. <BR>\n" );
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document.write( "Let w = width<BR>\n" );
document.write( "then<BR>\n" );
document.write( "w+2 = length<BR>\n" );
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document.write( "applying Pythagorean's theorem:<BR>\n" );
document.write( "w^2 + (w+2)^2 = 15<BR>\n" );
document.write( "w^2 + (w+2)(w+2) = 15<BR>\n" );
document.write( "w^2 + w^2+4w+4 = 15<BR>\n" );
document.write( "2w^2+4w+4 = 15<BR>\n" );
document.write( "2w^2+4w-11 = 0<BR>\n" );
document.write( "applying the quadratic formula we get:<BR>\n" );
document.write( "w = 1.55 m (width)<BR>\n" );
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document.write( "Length:<BR>\n" );
document.write( "w+2 = 1.55+2 = 3.55 m (length)<BR>\n" );
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document.write( "Dimensions are:<BR>\n" );
document.write( "1.55m by 3.55 m<BR>\n" );
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document.write( "Details of quadratic formula:<BR>\n" );
document.write( "<TABLE  BORDER=1>\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=2w%5E2%2B4w%2B-11+=+0 ALIGN=MIDDLE  ALT=\"2w%5E2%2B4w%2B-11+=+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=%284%29%5E2-4%2A2%2A-11=104 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%284%29%5E2-4%2A2%2A-11=104\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=104 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+=+%28-4%2B-sqrt%28+104+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-4%2B-sqrt%28+104+%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-%284%29%2Bsqrt%28+104+%29%29%2F2%5C2+=+1.54950975679639 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%284%29%2Bsqrt%28+104+%29%29%2F2%5C2+=+1.54950975679639\"   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-%284%29-sqrt%28+104+%29%29%2F2%5C2+=+-3.54950975679639 ALIGN=MIDDLE  ALT=\"w%5B2%5D+=+%28-%284%29-sqrt%28+104+%29%29%2F2%5C2+=+-3.54950975679639\"   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=2w%5E2%2B4w%2B-11 ALIGN=MIDDLE  ALT=\"2w%5E2%2B4w%2B-11\"   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=2w%5E2%2B4w%2B-11+=+2%28w-1.54950975679639%29%2A%28w--3.54950975679639%29 ALIGN=MIDDLE  ALT=\"2w%5E2%2B4w%2B-11+=+2%28w-1.54950975679639%29%2A%28w--3.54950975679639%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.54950975679639, -3.54950975679639.\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%2B4%2Ax%2B-11+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-11+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );