document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132818>Question 132818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello<BR>\n" );
document.write( "I hope someone can help me. Here is the question: THe position of an object moving in a straight line is given by s= 2t^2 - 3t, where s is in meters and t is the time in seconds the object has been in motion. How long (to the nearest tenth) wiil it take the object to move 17 meters?<BR>\n" );
document.write( "I am so lost! SO far what I have gotten from this is:<BR>\n" );
document.write( "17= 2t^2 - 3t<BR>\n" );
document.write( "2t^2 - 3t - 17= 0  But now what do I do? Please help-THank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97060 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=97060\">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=17=2t%5E2-3t ALIGN=MIDDLE  ALT=\"17=2t%5E2-3t\"   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=17=2t%5E2-3t ALIGN=MIDDLE  ALT=\"17=2t%5E2-3t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=17 ALIGN=MIDDLE  ALT=\"s=17\"   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=0=2t%5E2-3t-17 ALIGN=MIDDLE  ALT=\"0=2t%5E2-3t-17\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract 17 from both sides. \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( "Starting with the general quadratic\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\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%5E2-4%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;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2%2At%5E2-3%2At-17 ALIGN=MIDDLE  ALT=\"0=2%2At%5E2-3%2At-17\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-3 ALIGN=MIDDLE  ALT=\"b=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-17 ALIGN=MIDDLE  ALT=\"c=-17\"   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+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A-17+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"t+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A-17+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=-3, and c=-17\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A-17+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"t+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A-17+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -3 to get 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%283+%2B-+sqrt%28+9-4%2A2%2A-17+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"t+=+%283+%2B-+sqrt%28+9-4%2A2%2A-17+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -3 to get 9  (note: remember when you square -3, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E2=-3%2A-3=9 ALIGN=MIDDLE  ALT=\"%28-3%29%5E2=-3%2A-3=9\"   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+=+%283+%2B-+sqrt%28+9%2B136+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"t+=+%283+%2B-+sqrt%28+9%2B136+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-17%2A2 ALIGN=MIDDLE  ALT=\"-4%2A-17%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=136 ALIGN=MIDDLE  ALT=\"136\"   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+=+%283+%2B-+sqrt%28+145+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"t+=+%283+%2B-+sqrt%28+145+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%283+%2B-+sqrt%28145%29%29%2F4 ALIGN=MIDDLE  ALT=\"t+=+%283+%2B-+sqrt%28145%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%283+%2B+sqrt%28145%29%29%2F4 ALIGN=MIDDLE  ALT=\"t+=+%283+%2B+sqrt%28145%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%283+-+sqrt%28145%29%29%2F4 ALIGN=MIDDLE  ALT=\"t+=+%283+-+sqrt%28145%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3.76039864469807 ALIGN=MIDDLE  ALT=\"t=3.76039864469807\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2.26039864469807 ALIGN=MIDDLE  ALT=\"t=-2.26039864469807\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3.76039864469807 ALIGN=MIDDLE  ALT=\"t=3.76039864469807\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2.26039864469807 ALIGN=MIDDLE  ALT=\"t=-2.26039864469807\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, since a negative time doesn't make sense, our only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3.76039864469807 ALIGN=MIDDLE  ALT=\"t=3.76039864469807\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So it takes about 3.76 seconds for the object to move 17 meters\r<BR>\n" );
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document.write( " </SPAN>\n" );
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