document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=215011>Question 215011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to solve 42 = -21t + 4.9t^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162468 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=162468\">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=42+=+-21t+%2B+4.9t%5E2 ALIGN=MIDDLE  ALT=\"42+=+-21t+%2B+4.9t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=420+=+-210t+%2B+49t%5E2 ALIGN=MIDDLE  ALT=\"420+=+-210t+%2B+49t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by 10 to make every value a whole number.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-210t+%2B+49t%5E2-420 ALIGN=MIDDLE  ALT=\"0+=+-210t+%2B+49t%5E2-420\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 420 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+=+49t%5E2-210t-420 ALIGN=MIDDLE  ALT=\"0+=+49t%5E2-210t-420\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49t%5E2-210t-420 ALIGN=MIDDLE  ALT=\"49t%5E2-210t-420\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=At%5E2%2BBt%2BC ALIGN=MIDDLE  ALT=\"At%5E2%2BBt%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=49 ALIGN=MIDDLE  ALT=\"A=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-210 ALIGN=MIDDLE  ALT=\"B=-210\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-420 ALIGN=MIDDLE  ALT=\"C=-420\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula 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=t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%28-210%29+%2B-+sqrt%28+%28-210%29%5E2-4%2849%29%28-420%29+%29%29%2F%282%2849%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-%28-210%29+%2B-+sqrt%28+%28-210%29%5E2-4%2849%29%28-420%29+%29%29%2F%282%2849%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=49 ALIGN=MIDDLE  ALT=\"A=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-210 ALIGN=MIDDLE  ALT=\"B=-210\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-420 ALIGN=MIDDLE  ALT=\"C=-420\"   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+=+%28210+%2B-+sqrt%28+%28-210%29%5E2-4%2849%29%28-420%29+%29%29%2F%282%2849%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28210+%2B-+sqrt%28+%28-210%29%5E2-4%2849%29%28-420%29+%29%29%2F%282%2849%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-210 ALIGN=MIDDLE  ALT=\"-210\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210 ALIGN=MIDDLE  ALT=\"210\"   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+=+%28210+%2B-+sqrt%28+44100-4%2849%29%28-420%29+%29%29%2F%282%2849%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28210+%2B-+sqrt%28+44100-4%2849%29%28-420%29+%29%29%2F%282%2849%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-210 ALIGN=MIDDLE  ALT=\"-210\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44100 ALIGN=MIDDLE  ALT=\"44100\"   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+=+%28210+%2B-+sqrt%28+44100--82320+%29%29%2F%282%2849%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28210+%2B-+sqrt%28+44100--82320+%29%29%2F%282%2849%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2849%29%28-420%29 ALIGN=MIDDLE  ALT=\"4%2849%29%28-420%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-82320 ALIGN=MIDDLE  ALT=\"-82320\"   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+=+%28210+%2B-+sqrt%28+44100%2B82320+%29%29%2F%282%2849%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28210+%2B-+sqrt%28+44100%2B82320+%29%29%2F%282%2849%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2844100--82320%29 ALIGN=MIDDLE  ALT=\"sqrt%2844100--82320%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2844100%2B82320%29 ALIGN=MIDDLE  ALT=\"sqrt%2844100%2B82320%29\"   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+=+%28210+%2B-+sqrt%28+126420+%29%29%2F%282%2849%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28210+%2B-+sqrt%28+126420+%29%29%2F%282%2849%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44100 ALIGN=MIDDLE  ALT=\"44100\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=82320 ALIGN=MIDDLE  ALT=\"82320\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126420 ALIGN=MIDDLE  ALT=\"126420\"   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+=+%28210+%2B-+sqrt%28+126420+%29%29%2F%2898%29 ALIGN=MIDDLE  ALT=\"t+=+%28210+%2B-+sqrt%28+126420+%29%29%2F%2898%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49 ALIGN=MIDDLE  ALT=\"49\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=98 ALIGN=MIDDLE  ALT=\"98\"   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+=+%28210+%2B-+14%2Asqrt%28645%29%29%2F%2898%29 ALIGN=MIDDLE  ALT=\"t+=+%28210+%2B-+14%2Asqrt%28645%29%29%2F%2898%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28210%2B14%2Asqrt%28645%29%29%2F%2898%29 ALIGN=MIDDLE  ALT=\"t+=+%28210%2B14%2Asqrt%28645%29%29%2F%2898%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28210-14%2Asqrt%28645%29%29%2F%2898%29 ALIGN=MIDDLE  ALT=\"t+=+%28210-14%2Asqrt%28645%29%29%2F%2898%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28210%2B14%2Asqrt%28645%29%29%2F%2898%29 ALIGN=MIDDLE  ALT=\"t+=+%28210%2B14%2Asqrt%28645%29%29%2F%2898%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28210-14%2Asqrt%28645%29%29%2F%2898%29 ALIGN=MIDDLE  ALT=\"t+=+%28210-14%2Asqrt%28645%29%29%2F%2898%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "which approximate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5.771 ALIGN=MIDDLE  ALT=\"t=5.771\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-1.485 ALIGN=MIDDLE  ALT=\"t=-1.485\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "I'm assuming that the variable 't' is time. If so, then just ignore the second solution (as a negative time doesn't make sense).<BR>\n" );
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