document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170965>Question 170965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a real or imaginary solution\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "86. 3v^2 + 4v - 1 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126216 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=126216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\n" );
document.write( "\n" );
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 v:<BR><BR>\n" );
document.write( "\n" );
document.write( "  <BR>\n" );
document.write( "  Starting with the general quadratic<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=av%5E2%2Bbv%2Bc=0 ALIGN=MIDDLE  ALT=\"av%5E2%2Bbv%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  the general solution using the quadratic equation is:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"v+=+%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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Av%5E2%2B4%2Av-1=0 ALIGN=MIDDLE  ALT=\"3%2Av%5E2%2B4%2Av-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-1 ALIGN=MIDDLE  ALT=\"c=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A3%2A-1+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"v+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A3%2A-1+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=3, b=4, and c=-1<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+%28-4+%2B-+sqrt%28+16-4%2A3%2A-1+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"v+=+%28-4+%2B-+sqrt%28+16-4%2A3%2A-1+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 4 to get 16  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+%28-4+%2B-+sqrt%28+16%2B12+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"v+=+%28-4+%2B-+sqrt%28+16%2B12+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-1%2A3 ALIGN=MIDDLE  ALT=\"-4%2A-1%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+%28-4+%2B-+sqrt%28+28+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"v+=+%28-4+%2B-+sqrt%28+28+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+%28-4+%2B-+2%2Asqrt%287%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"v+=+%28-4+%2B-+2%2Asqrt%287%29%29%2F%282%2A3%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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+%28-4+%2B-+2%2Asqrt%287%29%29%2F6 ALIGN=MIDDLE  ALT=\"v+=+%28-4+%2B-+2%2Asqrt%287%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 3 to get 6<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So now the expression breaks down into two parts<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+%28-4+%2B+2%2Asqrt%287%29%29%2F6 ALIGN=MIDDLE  ALT=\"v+=+%28-4+%2B+2%2Asqrt%287%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+%28-4+-+2%2Asqrt%287%29%29%2F6 ALIGN=MIDDLE  ALT=\"v+=+%28-4+-+2%2Asqrt%287%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now break up the fraction<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=-4%2F6%2B2%2Asqrt%287%29%2F6 ALIGN=MIDDLE  ALT=\"v=-4%2F6%2B2%2Asqrt%287%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=-4%2F6-2%2Asqrt%287%29%2F6 ALIGN=MIDDLE  ALT=\"v=-4%2F6-2%2Asqrt%287%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Simplify<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=-2%2F3%2Bsqrt%287%29%2F3 ALIGN=MIDDLE  ALT=\"v=-2%2F3%2Bsqrt%287%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=-2%2F3-sqrt%287%29%2F3 ALIGN=MIDDLE  ALT=\"v=-2%2F3-sqrt%287%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So the solutions are:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=-2%2F3%2Bsqrt%287%29%2F3 ALIGN=MIDDLE  ALT=\"v=-2%2F3%2Bsqrt%287%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=-2%2F3-sqrt%287%29%2F3 ALIGN=MIDDLE  ALT=\"v=-2%2F3-sqrt%287%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );