document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066884>Question 1066884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a&#8203; round-robin chess&#8203; tournament, each player is paired with every other player once. The&#8203; function, shown&#8203; below, models the number of chess&#8203; games, N, that must be played in a&#8203; round-robin tournament with t chess players. In a&#8203; round-robin chess&#8203; tournament, 6 games were played. How many players entered the&#8203;tournament?\r<BR>\n" );
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document.write( "how to solve formula? N=t^2-t / 2<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 #682110 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=682110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+%28t%5E2-t%29%2F2 ALIGN=MIDDLE  ALT=\"N+=+%28t%5E2-t%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+%28t%5E2-t%29%2F2 ALIGN=MIDDLE  ALT=\"6+=+%28t%5E2-t%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace N with 6. The goal is to solve for t.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A6+=+2%2A%28%28t%5E2-t%29%2F2%29 ALIGN=MIDDLE  ALT=\"2%2A6+=+2%2A%28%28t%5E2-t%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+t%5E2-t ALIGN=MIDDLE  ALT=\"12+=+t%5E2-t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-12+=+t%5E2-t-12 ALIGN=MIDDLE  ALT=\"12-12+=+t%5E2-t-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 12 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+t%5E2-t-12 ALIGN=MIDDLE  ALT=\"0+=+t%5E2-t-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-t-12+=+0 ALIGN=MIDDLE  ALT=\"t%5E2-t-12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t-4%29%28t%2B3%29+=+0 ALIGN=MIDDLE  ALT=\"%28t-4%29%28t%2B3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-4=0 ALIGN=MIDDLE  ALT=\"t-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2B3=0 ALIGN=MIDDLE  ALT=\"t%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4 ALIGN=MIDDLE  ALT=\"t=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-3 ALIGN=MIDDLE  ALT=\"t=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Ignore the negative solution since it makes no sense to have -3 players.\r<BR>\n" );
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document.write( "The only practical solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+4 ALIGN=MIDDLE  ALT=\"t+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There are 4 players in the tournament. </SPAN>\n" );
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