document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171781>Question 171781</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078228808/algebrahomeworkh>Geometry: Integration, Application and Connections</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> There is a rectangle with 2 diagonals.  The diagonals are RT and QS with intersection C. The problem gives you RT as 3xsquared and QC as 5x+4. Thye want you to find the  value of x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126890 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=126890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> My appologies to Nerdy Bill but the solution is a bit off.<BR>\n" );
document.write( "From the description of the rectangle and its diagonals, the one diagonal is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RT+=+3x%5E2 ALIGN=MIDDLE  ALT=\"RT+=+3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > but the other diagonal QS is really given as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QC+=+5x%2B4 ALIGN=MIDDLE  ALT=\"QC+=+5x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this is but half of the complete diagonal QS, so the equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RT+=+2QC ALIGN=MIDDLE  ALT=\"RT+=+2QC\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+=+2%285x%2B4%29 ALIGN=MIDDLE  ALT=\"3x%5E2+=+2%285x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewriting this it becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-10x-8+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2-10x-8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...and this is factorable to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B2%29%28x-4%29+=+0 ALIGN=MIDDLE  ALT=\"%283x%2B2%29%28x-4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2%2F3 ALIGN=MIDDLE  ALT=\"x+=+-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and, as you pointed out, you can discard the negative quantity as we are talking about lengths, so...<BR>\n" );
document.write( "x = 4\r<BR>\n" );
document.write( "\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+=+3%284%29%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2+=+3%284%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2816%29+=+48 ALIGN=MIDDLE  ALT=\"3%2816%29+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%285x%2B4%29+=+2%2820%2B4%29 ALIGN=MIDDLE  ALT=\"2%285x%2B4%29+=+2%2820%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2824%29+=+48 ALIGN=MIDDLE  ALT=\"2%2824%29+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );