document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=875278>Question 875278</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help in solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5%2Bx%2F3=1%2Fx ALIGN=MIDDLE  ALT=\"2%2F5%2Bx%2F3=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #528095 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=528095\">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=2%2F5%2Bx%2F3=1%2Fx ALIGN=MIDDLE  ALT=\"2%2F5%2Bx%2F3=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "We could say we use a common denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A3%2Ax=15x ALIGN=MIDDLE  ALT=\"5%2A3%2Ax=15x\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5%2Bx%2F3=1%2Fx ALIGN=MIDDLE  ALT=\"2%2F5%2Bx%2F3=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2F15x%2B5x%5E2%2F15x=15%2F15x ALIGN=MIDDLE  ALT=\"6x%2F15x%2B5x%5E2%2F15x=15%2F15x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%2B5x%5E2%29%2F15x=15%2F15x ALIGN=MIDDLE  ALT=\"%286x%2B5x%5E2%29%2F15x=15%2F15x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B5x%5E2=15 ALIGN=MIDDLE  ALT=\"6x%2B5x%5E2=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Or we could say that we multiply times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A3%2Ax=15x ALIGN=MIDDLE  ALT=\"5%2A3%2Ax=15x\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5%2Bx%2F3=1%2Fx ALIGN=MIDDLE  ALT=\"2%2F5%2Bx%2F3=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%282%2F5%2Bx%2F3%29=15x%281%2Fx%29 ALIGN=MIDDLE  ALT=\"15x%282%2F5%2Bx%2F3%29=15x%281%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%282%2F5%29%2B15x%28x%2F3%29=15x%2Fx ALIGN=MIDDLE  ALT=\"15x%282%2F5%29%2B15x%28x%2F3%29=15x%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30x%2F5%2B15x%5E2%2F3=15 ALIGN=MIDDLE  ALT=\"30x%2F5%2B15x%5E2%2F3=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B5x%5E2=15 ALIGN=MIDDLE  ALT=\"6x%2B5x%5E2=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "It's the same thing, we end up with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B5x%5E2=15 ALIGN=MIDDLE  ALT=\"6x%2B5x%5E2=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B5x%5E2-15=0 ALIGN=MIDDLE  ALT=\"6x%2B5x%5E2-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B6x-15=0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B6x-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > anyway,<BR>\n" );
document.write( "and now we have to solve that quadratic equation.<BR>\n" );
document.write( "Factoring does not work, so we have two options to solve that equation:<BR>\n" );
document.write( " <BR>\n" );
document.write( "USING THE QUADRATIC FORMULA:<BR>\n" );
document.write( "The quadratic formula says that the solutions (real or imaginary) of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > are given by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%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( "In the case of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B6x-15=0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B6x-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   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=-15 ALIGN=MIDDLE  ALT=\"c=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-6+%2B-+sqrt%286%5E2-4%2A5%2A%28-15%29+%29%29%2F%282%2A5%29=%28-6+%2B-+sqrt%2836%2B300%29%29%2F10=%28-6+%2B-+sqrt%28336%29%29%2F10 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That can be simplified as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-6+%2B-+sqrt%2816%2A21%29%29%2F10=%28-6+%2B-+sqrt%2816%29%2Asqrt%2821%29%29%2F10=%28-6+%2B-+4sqrt%2821%29%29%2F10=%28-3+%2B-+2sqrt%2821%29%29%2F5 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "COMPLETING THE SQUARE:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B6x-15=0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B6x-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B6x=15 ALIGN=MIDDLE  ALT=\"5x%5E2%2B6x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2%2B6x%29%2F5=15%2F5 ALIGN=MIDDLE  ALT=\"%285x%5E2%2B6x%29%2F5=15%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%286%2F5%29x=3 ALIGN=MIDDLE  ALT=\"x%5E2%2B%286%2F5%29x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2%283%2F5%29x%2B%283%2F5%29%5E2=3%2B%283%2F5%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B2%283%2F5%29x%2B%283%2F5%29%5E2=3%2B%283%2F5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%2F5%29%5E2=75%2F25%2B9%2F25 ALIGN=MIDDLE  ALT=\"%28x%2B3%2F5%29%5E2=75%2F25%2B9%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%2F5%29%5E2=84%2F25 ALIGN=MIDDLE  ALT=\"%28x%2B3%2F5%29%5E2=84%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2F5=sqrt%2884%2F25%29=sqrt%284%2A21%29%2Fsqrt%2825%29=sqrt%284%29sqrt%2821%29%2F5=2sqrt%2821%29%2F5 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2F5=-2sqrt%2821%29%2F5 ALIGN=MIDDLE  ALT=\"x%2B3%2F5=-2sqrt%2821%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2F5=2sqrt%2821%29%2F5 ALIGN=MIDDLE  ALT=\"x%2B3%2F5=2sqrt%2821%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F5%2B2sqrt%2821%29%2F5=%28-3%2B2sqrt%2821%29%295 ALIGN=MIDDLE  ALT=\"x=-3%2F5%2B2sqrt%2821%29%2F5=%28-3%2B2sqrt%2821%29%295\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2F5=-2sqrt%2821%29%2F5 ALIGN=MIDDLE  ALT=\"x%2B3%2F5=-2sqrt%2821%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F5-2sqrt%2821%29%2F5=%28-3-2sqrt%2821%29%295 ALIGN=MIDDLE  ALT=\"x=-3%2F5-2sqrt%2821%29%2F5=%28-3-2sqrt%2821%29%295\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and both solutions can be expressed as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-3+%2B-+2sqrt%2821%29%29%2F5 ALIGN=MIDDLE  ALT=\"x=%28-3+%2B-+2sqrt%2821%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );