document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88652>Question 88652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5/2t-t=3+3/2t </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64441 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=64441\">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=5%2F2t-t=3%2B3%2F2t ALIGN=MIDDLE  ALT=\"5%2F2t-t=3%2B3%2F2t\"   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=2t%285%2F2t-t%29=2t%283%2B3%2F2t%29 ALIGN=MIDDLE  ALT=\"2t%285%2F2t-t%29=2t%283%2B3%2F2t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 2t\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-2t%5E2=6t%2B3 ALIGN=MIDDLE  ALT=\"5-2t%5E2=6t%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-2t%5E2-6t-3=0 ALIGN=MIDDLE  ALT=\"5-2t%5E2-6t-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get everything to one side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2t%5E2-6t%2B2=0 ALIGN=MIDDLE  ALT=\"-2t%5E2-6t%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Now 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=-2%2At%5E2-6%2At%2B2=0 ALIGN=MIDDLE  ALT=\"-2%2At%5E2-6%2At%2B2=0\"   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=-6 ALIGN=MIDDLE  ALT=\"b=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=2 ALIGN=MIDDLE  ALT=\"c=2\"   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--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A-2%2A2+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"t+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A-2%2A2+%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-2, b=-6, and c=2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A-2%2A2+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"t+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A-2%2A2+%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -6 to get 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%286+%2B-+sqrt%28+36-4%2A-2%2A2+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"t+=+%286+%2B-+sqrt%28+36-4%2A-2%2A2+%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -6 to get 36\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%286+%2B-+sqrt%28+36%2B16+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"t+=+%286+%2B-+sqrt%28+36%2B16+%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A2%2A-2 ALIGN=MIDDLE  ALT=\"-4%2A2%2A-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   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+=+%286+%2B-+sqrt%28+52+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"t+=+%286+%2B-+sqrt%28+52+%29%29%2F%282%2A-2%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+=+%286+%2B-+2%2Asqrt%2813%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"t+=+%286+%2B-+2%2Asqrt%2813%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify 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+=+%286+%2B-+2%2Asqrt%2813%29%29%2F-4 ALIGN=MIDDLE  ALT=\"t+=+%286+%2B-+2%2Asqrt%2813%29%29%2F-4\"   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+=+%286+%2B+2%2Asqrt%2813%29%29%2F-4 ALIGN=MIDDLE  ALT=\"t+=+%286+%2B+2%2Asqrt%2813%29%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%286+-+2%2Asqrt%2813%29%29%2F-4 ALIGN=MIDDLE  ALT=\"t+=+%286+-+2%2Asqrt%2813%29%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which split up to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%2B6%2F-4%2B2%2Asqrt%2813%29%2F-4 ALIGN=MIDDLE  ALT=\"t=%2B6%2F-4%2B2%2Asqrt%2813%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%2B6%2F-4%2B2%2Asqrt%2813%29%2F-4 ALIGN=MIDDLE  ALT=\"t=%2B6%2F-4%2B2%2Asqrt%2813%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and simplify to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-3+%2F+2-sqrt%2813%29%2F+2 ALIGN=MIDDLE  ALT=\"t=-3+%2F+2-sqrt%2813%29%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-3+%2F+2%2B+sqrt%2813%29%2F+2 ALIGN=MIDDLE  ALT=\"t=-3+%2F+2%2B+sqrt%2813%29%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-3.30277563773199 ALIGN=MIDDLE  ALT=\"t=-3.30277563773199\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0.302775637731995 ALIGN=MIDDLE  ALT=\"t=0.302775637731995\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-3.30277563773199 ALIGN=MIDDLE  ALT=\"t=-3.30277563773199\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0.302775637731995 ALIGN=MIDDLE  ALT=\"t=0.302775637731995\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Ax%5E2-6%2Ax%2B2 ALIGN=MIDDLE  ALT=\"-2%2Ax%5E2-6%2Ax%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just replace t with x), we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-13.302775637732%2C+10.302775637732%2C+-13.302775637732%2C+10.302775637732%2C-2%2Ax%5E2%2B-6%2Ax%2B2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when we use the root finder feature on a calculator, we find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3.30277563773199 ALIGN=MIDDLE  ALT=\"x=-3.30277563773199\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.302775637731995 ALIGN=MIDDLE  ALT=\"x=0.302775637731995\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer </SPAN>\n" );
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