document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196644>Question 196644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I keep getting the incorrect answer to the following problem, I'm not sure where my error was, can you help me?\r<BR>\n" );
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document.write( "A large pond is stocked with fish. The fish population P is modeled by the formula P = 4t + 8&#8730;t + 110, where t is the number of days since the fish were first introduced into the pond. How many days will it take for the fish population to reach 500?\r<BR>\n" );
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document.write( "thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147509 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=147509\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4t+8sqrt(t)+110=500<BR>\n" );
document.write( "4t-390=-8sqrt(t)<BR>\n" );
document.write( "2t-195=-4sqrt(t)<BR>\n" );
document.write( "4t^2-780t+38025=16t<BR>\n" );
document.write( "4t^2-796t+380256=0<BR>\n" );
document.write( "t=79.65 days Answer. Quadratic equation. [t=119.35 is extraneous]<BR>\n" );
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document.write( "Ed<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C140%2C-100%2C600%2C4x%2B%288%2Asqrt%28x%29%29%2B110%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C140%2C-100%2C600%2C4x%2B%288%2Asqrt%28x%29%29%2B110%29\"   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=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B-796x%2B38025+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-796x%2B38025+=+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=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%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=%28-796%29%5E2-4%2A4%2A38025=25216 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-796%29%5E2-4%2A4%2A38025=25216\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=25216 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--796%2B-sqrt%28+25216+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--796%2B-sqrt%28+25216+%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=x%5B1%5D+=+%28-%28-796%29%2Bsqrt%28+25216+%29%29%2F2%5C4+=+119.349433241279 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-796%29%2Bsqrt%28+25216+%29%29%2F2%5C4+=+119.349433241279\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-796%29-sqrt%28+25216+%29%29%2F2%5C4+=+79.6505667587208 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-796%29-sqrt%28+25216+%29%29%2F2%5C4+=+79.6505667587208\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B-796x%2B38025 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-796x%2B38025\"   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=4x%5E2%2B-796x%2B38025+=+4%28x-119.349433241279%29%2A%28x-79.6505667587208%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-796x%2B38025+=+4%28x-119.349433241279%29%2A%28x-79.6505667587208%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 119.349433241279, 79.6505667587208.\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+4%2Ax%5E2%2B-796%2Ax%2B38025+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-796%2Ax%2B38025+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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