document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=292942>Question 292942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 16t^2= 24t + 15  Solve for t </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #211478 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=211478\">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=16t%5E2=+24t+%2B+15 ALIGN=MIDDLE  ALT=\"16t%5E2=+24t+%2B+15\"   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%5E2-24t-15=0 ALIGN=MIDDLE  ALT=\"16t%5E2-24t-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get everything to one side.\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for t:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<BR>\n" );
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document.write( "  the general solution using the quadratic equation is:<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;\" ><BR>\n" );
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document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2At%5E2-24%2At-15=0 ALIGN=MIDDLE  ALT=\"16%2At%5E2-24%2At-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <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=-24 ALIGN=MIDDLE  ALT=\"b=-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-15 ALIGN=MIDDLE  ALT=\"c=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28--24+%2B-+sqrt%28+%28-24%29%5E2-4%2A16%2A-15+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%28--24+%2B-+sqrt%28+%28-24%29%5E2-4%2A16%2A-15+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=16, b=-24, and c=-15<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2824+%2B-+sqrt%28+%28-24%29%5E2-4%2A16%2A-15+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%2824+%2B-+sqrt%28+%28-24%29%5E2-4%2A16%2A-15+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -24 to get 24<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2824+%2B-+sqrt%28+576-4%2A16%2A-15+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%2824+%2B-+sqrt%28+576-4%2A16%2A-15+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -24 to get 576  (note: remember when you square -24, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-24%29%5E2=-24%2A-24=576 ALIGN=MIDDLE  ALT=\"%28-24%29%5E2=-24%2A-24=576\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2824+%2B-+sqrt%28+576%2B960+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%2824+%2B-+sqrt%28+576%2B960+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-15%2A16 ALIGN=MIDDLE  ALT=\"-4%2A-15%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=960 ALIGN=MIDDLE  ALT=\"960\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2824+%2B-+sqrt%28+1536+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%2824+%2B-+sqrt%28+1536+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2824+%2B-+16%2Asqrt%286%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%2824+%2B-+16%2Asqrt%286%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2824+%2B-+16%2Asqrt%286%29%29%2F32 ALIGN=MIDDLE  ALT=\"t+=+%2824+%2B-+16%2Asqrt%286%29%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 16 to get 32<BR>\n" );
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document.write( "  So now the expression breaks down into two parts<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2824+%2B+16%2Asqrt%286%29%29%2F32 ALIGN=MIDDLE  ALT=\"t+=+%2824+%2B+16%2Asqrt%286%29%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2824+-+16%2Asqrt%286%29%29%2F32 ALIGN=MIDDLE  ALT=\"t+=+%2824+-+16%2Asqrt%286%29%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now break up the fraction<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%2B24%2F32%2B16%2Asqrt%286%29%2F32 ALIGN=MIDDLE  ALT=\"t=%2B24%2F32%2B16%2Asqrt%286%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%2B24%2F32-16%2Asqrt%286%29%2F32 ALIGN=MIDDLE  ALT=\"t=%2B24%2F32-16%2Asqrt%286%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Simplify<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3%2F4%2Bsqrt%286%29%2F2 ALIGN=MIDDLE  ALT=\"t=3%2F4%2Bsqrt%286%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3%2F4-sqrt%286%29%2F2 ALIGN=MIDDLE  ALT=\"t=3%2F4-sqrt%286%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So the solutions are:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3%2F4%2Bsqrt%286%29%2F2 ALIGN=MIDDLE  ALT=\"t=3%2F4%2Bsqrt%286%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3%2F4-sqrt%286%29%2F2 ALIGN=MIDDLE  ALT=\"t=3%2F4-sqrt%286%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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