document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=580570>Question 580570</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 0=-16t^2+104t+56 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371388 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=371388\">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=0=-16t%5E2%2B104t%2B56 ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B104t%2B56\"   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=-16t%5E2%2B104t%2B56=0 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B104t%2B56=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16t%5E2-104t-56=0 ALIGN=MIDDLE  ALT=\"16t%5E2-104t-56=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply every term by -1 to make the leading coefficient positive.\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=16t%5E2-104t-56 ALIGN=MIDDLE  ALT=\"16t%5E2-104t-56\"   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=16 ALIGN=MIDDLE  ALT=\"A=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-104 ALIGN=MIDDLE  ALT=\"B=-104\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-56 ALIGN=MIDDLE  ALT=\"C=-56\"   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-%28-104%29+%2B-+sqrt%28+%28-104%29%5E2-4%2816%29%28-56%29+%29%29%2F%282%2816%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-%28-104%29+%2B-+sqrt%28+%28-104%29%5E2-4%2816%29%28-56%29+%29%29%2F%282%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=16 ALIGN=MIDDLE  ALT=\"A=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-104 ALIGN=MIDDLE  ALT=\"B=-104\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-56 ALIGN=MIDDLE  ALT=\"C=-56\"   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+=+%28104+%2B-+sqrt%28+%28-104%29%5E2-4%2816%29%28-56%29+%29%29%2F%282%2816%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28104+%2B-+sqrt%28+%28-104%29%5E2-4%2816%29%28-56%29+%29%29%2F%282%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-104 ALIGN=MIDDLE  ALT=\"-104\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=104 ALIGN=MIDDLE  ALT=\"104\"   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+=+%28104+%2B-+sqrt%28+10816-4%2816%29%28-56%29+%29%29%2F%282%2816%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28104+%2B-+sqrt%28+10816-4%2816%29%28-56%29+%29%29%2F%282%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-104 ALIGN=MIDDLE  ALT=\"-104\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10816 ALIGN=MIDDLE  ALT=\"10816\"   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+=+%28104+%2B-+sqrt%28+10816--3584+%29%29%2F%282%2816%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28104+%2B-+sqrt%28+10816--3584+%29%29%2F%282%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2816%29%28-56%29 ALIGN=MIDDLE  ALT=\"4%2816%29%28-56%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3584 ALIGN=MIDDLE  ALT=\"-3584\"   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+=+%28104+%2B-+sqrt%28+10816%2B3584+%29%29%2F%282%2816%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28104+%2B-+sqrt%28+10816%2B3584+%29%29%2F%282%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810816--3584%29 ALIGN=MIDDLE  ALT=\"sqrt%2810816--3584%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810816%2B3584%29 ALIGN=MIDDLE  ALT=\"sqrt%2810816%2B3584%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+=+%28104+%2B-+sqrt%28+14400+%29%29%2F%282%2816%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28104+%2B-+sqrt%28+14400+%29%29%2F%282%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10816 ALIGN=MIDDLE  ALT=\"10816\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3584 ALIGN=MIDDLE  ALT=\"3584\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14400 ALIGN=MIDDLE  ALT=\"14400\"   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+=+%28104+%2B-+sqrt%28+14400+%29%29%2F%2832%29 ALIGN=MIDDLE  ALT=\"t+=+%28104+%2B-+sqrt%28+14400+%29%29%2F%2832%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=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   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+=+%28104+%2B-+120%29%2F%2832%29 ALIGN=MIDDLE  ALT=\"t+=+%28104+%2B-+120%29%2F%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14400 ALIGN=MIDDLE  ALT=\"14400\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120 ALIGN=MIDDLE  ALT=\"120\"   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+=+%28104+%2B+120%29%2F%2832%29 ALIGN=MIDDLE  ALT=\"t+=+%28104+%2B+120%29%2F%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28104+-+120%29%2F%2832%29 ALIGN=MIDDLE  ALT=\"t+=+%28104+-+120%29%2F%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28224%29%2F%2832%29 ALIGN=MIDDLE  ALT=\"t+=+%28224%29%2F%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=++%28-16%29%2F%2832%29 ALIGN=MIDDLE  ALT=\"t+=++%28-16%29%2F%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+7 ALIGN=MIDDLE  ALT=\"t+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-1%2F2 ALIGN=MIDDLE  ALT=\"t+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \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+=+7 ALIGN=MIDDLE  ALT=\"t+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-1%2F2 ALIGN=MIDDLE  ALT=\"t+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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