document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74153>Question 74153</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618503072/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I can't quite figure this one out. The value for t=6 but I can't see how we get there. Greg <BR>\n" );
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document.write( "               t squared-t/2=15 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53186 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=53186\">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=%28t%5E2-t%29%2F2=15 ALIGN=MIDDLE  ALT=\"%28t%5E2-t%29%2F2=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >Start with the given equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29t%5E2-%281%2F2%29t=15 ALIGN=MIDDLE  ALT=\"%281%2F2%29t%5E2-%281%2F2%29t=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >Rewrite the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29t%5E2-%281%2F2%29t-15=0 ALIGN=MIDDLE  ALT=\"%281%2F2%29t%5E2-%281%2F2%29t-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >Get all terms to one side. Now we can solve for t by using the quadratic formula<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=at%5E2%2Bbt%2Bc=0 ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5t%5E2%2B-0.5t%2B-15+=+0 ALIGN=MIDDLE  ALT=\"0.5t%5E2%2B-0.5t%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=t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"t%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=%28-0.5%29%5E2-4%2A0.5%2A-15=30.25 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-0.5%29%5E2-4%2A0.5%2A-15=30.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=30.25 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--0.5%2B-sqrt%28+30.25+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--0.5%2B-sqrt%28+30.25+%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=t%5B1%5D+=+%28-%28-0.5%29%2Bsqrt%28+30.25+%29%29%2F2%5C0.5+=+6 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%28-0.5%29%2Bsqrt%28+30.25+%29%29%2F2%5C0.5+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D+=+%28-%28-0.5%29-sqrt%28+30.25+%29%29%2F2%5C0.5+=+-5 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%28-0.5%29-sqrt%28+30.25+%29%29%2F2%5C0.5+=+-5\"   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=0.5t%5E2%2B-0.5t%2B-15 ALIGN=MIDDLE  ALT=\"0.5t%5E2%2B-0.5t%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=0.5t%5E2%2B-0.5t%2B-15+=+0.5%28t-6%29%2A%28t--5%29 ALIGN=MIDDLE  ALT=\"0.5t%5E2%2B-0.5t%2B-15+=+0.5%28t-6%29%2A%28t--5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6, -5.\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+0.5%2Ax%5E2%2B-0.5%2Ax%2B-15+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.5%2Ax%5E2%2B-0.5%2Ax%2B-15+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "So t=-5 and t=6 </SPAN>\n" );
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