document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=800723>Question 800723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, my word problem is\r<BR>\n" );
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document.write( "A population of crocodile is a game reserve after t years can be modelled by the equation 42t^2+36t+1008. after how may years will the population be equal to 1620?  use the formula t= -5+-sqrt(b^2-4ac)/2.\r<BR>\n" );
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document.write( "I have done the problem to where I get 36+-sqrt(-168048)/84 and know I don't know how to complete this problem any further.  my e-mail address is; dejagero@gmail.com\r<BR>\n" );
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document.write( "I will appreciate your help, I hae sleepless knight over this problem  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #483222 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=483222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula given is not for applying blindly to a polynomial.<BR>\n" );
document.write( "It is used to apply to a quadratic equation of the form <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;\" >,<BR>\n" );
document.write( "meaning an equation that says that a quadratic polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28equals%29 ALIGN=MIDDLE  ALT=\"highlight%28equals%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28zero%29 ALIGN=MIDDLE  ALT=\"highlight%28zero%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "To get from your problem to such an equation, whose solutions would be given by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you have to start by stating (in algebra language) that the population equals 1620,<BR>\n" );
document.write( "and then do some manipulation to get to the form <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;\" > with that zero on one side of the equal sign.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42t%5E2%2B36t%2B1008=1620 ALIGN=MIDDLE  ALT=\"42t%5E2%2B36t%2B1008=1620\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42t%5E2%2B36t%2B1008-1620=0 ALIGN=MIDDLE  ALT=\"42t%5E2%2B36t%2B1008-1620=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42t%5E2%2B36t-612=0 ALIGN=MIDDLE  ALT=\"42t%5E2%2B36t-612=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-612 ALIGN=MIDDLE  ALT=\"-612\"   DISABLED_style= \"max-width:90%; height:auto;\" > term without <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > being opposite in sign to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42 ALIGN=MIDDLE  ALT=\"42\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > you are assured to get a positive number under the square root.<BR>\n" );
document.write( "Also, at any point in the line above, you could realize that everything is divisible by 6, and dividing by 6 makes the numbers smaller.<BR>\n" );
document.write( "For example,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42t%5E2%2B36t-612=0 ALIGN=MIDDLE  ALT=\"42t%5E2%2B36t-612=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2842t%5E2%2B36t-612%29%2F6=0%2F6 ALIGN=MIDDLE  ALT=\"%2842t%5E2%2B36t-612%29%2F6=0%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2842t%5E2%2B36t-612%29%2F6=0%2F6 ALIGN=MIDDLE  ALT=\"%2842t%5E2%2B36t-612%29%2F6=0%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7t%5E2%2B6t-102=0 ALIGN=MIDDLE  ALT=\"7t%5E2%2B6t-102=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That simplification is not absolutely needed, but helps if you are prone to make mistakes when writing long numbers.<BR>\n" );
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document.write( "Then, you apply the formula, but the minus sign in front of the square root will give you a negative result, which would not make sense for the problem, so the useful result will be calculated as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-36%2Bsqrt%2836%5E2-4%2A42%2A%28-612%29%29%29%2F%282%2A42%29=+%28-36%2Bsqrt%281296%2B102816%29%29%2F84=+%28-36%2Bsqrt%28104112%29%29%2F84 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >= approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-36%2B322.66%29%2F84=286.66%2F84 ALIGN=MIDDLE  ALT=\"%28-36%2B322.66%29%2F84=286.66%2F84\"   DISABLED_style= \"max-width:90%; height:auto;\" >=approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.4 ALIGN=MIDDLE  ALT=\"3.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-6%2Bsqrt%286%5E2-4%2A7%2A%28-102%29%29%29%2F%282%2A7%29=+%28-6%2Bsqrt%2836%2B2856%29%29%2F14=%28-6%2Bsqrt%282892%29%29%2F14 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >= approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%2B53.78%29%2F84=47.78%2F14 ALIGN=MIDDLE  ALT=\"%28-6%2B53.78%29%2F84=47.78%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" >=approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.4 ALIGN=MIDDLE  ALT=\"3.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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