document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=819247>Question 819247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -3/10a^2+20a-80=a/5a-10+1/2a+8<BR>\n" );
document.write( "Please show me how to solve for \"a\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #493036 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=493036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -3/10a^2+20a-80=a/5a-10+1/2a+8 means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F10a%5E2%2B20a-80=a%2F5a-10%2B1%2F2a%2B8 ALIGN=MIDDLE  ALT=\"-3%2F10a%5E2%2B20a-80=a%2F5a-10%2B1%2F2a%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That would be a weird, difficult problem.<BR>\n" );
document.write( " <BR>\n" );
document.write( "I suspect you meant<BR>\n" );
document.write( "-3/(10a^2+20a-80)=a/(5a-10)+1/(2a+8)<BR>\n" );
document.write( "which you would write as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F%2810a%5E2%2B20a-80%29=a%2F%285a-10%29%2B1%2F%282a%2B8%29 ALIGN=MIDDLE  ALT=\"-3%2F%2810a%5E2%2B20a-80%29=a%2F%285a-10%29%2B1%2F%282a%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "when writing on paper,<BR>\n" );
document.write( "or maybe you would write it as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2F%2810a%5E2%2B20a-80%29=a%2F%285a-10%29%2B1%2F%282a%2B8%29 ALIGN=MIDDLE  ALT=\"%28-3%29%2F%2810a%5E2%2B20a-80%29=a%2F%285a-10%29%2B1%2F%282a%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(It's the same, but the minus sign next to the 3 may be more convenient).<BR>\n" );
document.write( "That is the problem I will solve for you.<BR>\n" );
document.write( "First, you need to realize that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285a-10%29%282a%2B8%29=10a%5E2%2B40a-20a-80=10a%5E2%2B20a-80 ALIGN=MIDDLE  ALT=\"%285a-10%29%282a%2B8%29=10a%5E2%2B40a-20a-80=10a%5E2%2B20a-80\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You could use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%5E2%2B20a-80 ALIGN=MIDDLE  ALT=\"10a%5E2%2B20a-80\"   DISABLED_style= \"max-width:90%; height:auto;\" > as your common denominator.<BR>\n" );
document.write( "(If your teacher likes that way of working through the problem, you may want to humor the teacher).<BR>\n" );
document.write( "Another option is to multiply both sides of the equal sign times<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285a-10%29%282a%2B8%29=10a%5E2%2B20a-80 ALIGN=MIDDLE  ALT=\"%285a-10%29%282a%2B8%29=10a%5E2%2B20a-80\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Multiplying both sides of the equal sign times a number or expression  gives you an equivalent equation,<BR>\n" );
document.write( "EXCEPT if the number or expression is zero.<BR>\n" );
document.write( "I would just multiply without worrying now, and later check the solutions found.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2810a%5E2%2B20a-80%29%2F%2810a%5E2%2B20a-80%29=%28a%2F%285a-10%29%2B1%2F%282a%2B8%29%29%285a-10%29%282a%2B8%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3=a%285a-10%29%282a%2B8%29%2F%285a-10%29%2B1%285a-10%29%282a%2B8%29%2F%282a%2B8%29 ALIGN=MIDDLE  ALT=\"-3=a%285a-10%29%282a%2B8%29%2F%285a-10%29%2B1%285a-10%29%282a%2B8%29%2F%282a%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3=a%282a%2B8%29%2B%285a-10%29 ALIGN=MIDDLE  ALT=\"-3=a%282a%2B8%29%2B%285a-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3=2a%5E2%2B8a%2B5a-10 ALIGN=MIDDLE  ALT=\"-3=2a%5E2%2B8a%2B5a-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2a%5E2%2B13a-10%2B3 ALIGN=MIDDLE  ALT=\"0=2a%5E2%2B13a-10%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2%2B13a-7=0 ALIGN=MIDDLE  ALT=\"2a%5E2%2B13a-7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we have to solve that quadratic equation.<BR>\n" );
document.write( "I would use factoring, starting by looking for factor pairs that multiply to give <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28-7%29=-14 ALIGN=MIDDLE  ALT=\"2%2A%28-7%29=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > and add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2A%28-1%29=-14 ALIGN=MIDDLE  ALT=\"14%2A%28-1%29=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2A%28-1%29=13 ALIGN=MIDDLE  ALT=\"14%2A%28-1%29=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > so I re-write the equation as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2%2B14a-a-7=0 ALIGN=MIDDLE  ALT=\"2a%5E2%2B14a-a-7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then factor by grouping:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282a%5E2-a%29%2B%2814a-7%29=0 ALIGN=MIDDLE  ALT=\"%282a%5E2-a%29%2B%2814a-7%29=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%282a-1%29%2B7%282a-1%29=0 ALIGN=MIDDLE  ALT=\"a%282a-1%29%2B7%282a-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B7%29%282a-1%29=0 ALIGN=MIDDLE  ALT=\"%28a%2B7%29%282a-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the solutions happen when<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B7=0 ALIGN=MIDDLE  ALT=\"a%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=-7%29 ALIGN=MIDDLE  ALT=\"highlight%28a=-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a-1=0 ALIGN=MIDDLE  ALT=\"2a-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=1%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28a=1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Neither one of those solutions makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285a-10%29%282a%2B8%29=10a%5E2%2B20a-80 ALIGN=MIDDLE  ALT=\"%285a-10%29%282a%2B8%29=10a%5E2%2B20a-80\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to zero,<BR>\n" );
document.write( "so we should accept those solutions, but it is good to verify.<BR>\n" );
document.write( "Verification:<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-7 ALIGN=MIDDLE  ALT=\"a=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2F%2810a%5E2%2B20a-80%29=%28-3%29%2F%2810%2A49%2B20%2A%28-7%29-80%29=%28-3%29%2F%28490-140-80%29=%28-3%29%2F270=-1%2F90 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%285a-10%29%2B1%2F%282a%2B8%29=%28-7%29%2F%285%28-7%29-10%29%2B1%2F%282%28-7%29%2B8%29=%28-7%29%2F%28-35-10%29%2B1%2F%28-14%2B8%29=%28-7%29%2F%28-45%29%2B1%2F%28-6%29=%28-7%292%2F%28-45%2A2%29%2B1%2A15%2F%28-6%2A15%29=14%2F90-15%2F90=-1%2F90 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1%2F2 ALIGN=MIDDLE  ALT=\"a=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2F%2810a%5E2%2B20a-80%29=%28-3%29%2F%2810%2A%281%2F4%29%2B20%2A%281%2F2%29-80%29=%28-3%29%2F%285%2F2%2B10-80%29=%28-3%29%2F%28-70%2B5%2F2%29=%28-3%29%2F%28-135%2F2%29=3%282%2F135%29=2%2F45 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%285a-10%29%2B1%2F%282a%2B8%29=%281%2F2%29%2F%285%281%2F2%29-10%29%2B1%2F%282%281%2F2%29%2B8%29=%28-7%29%2F%285%2F2-10%29%2B1%2F%281%2B8%29=%281%2F2%29%2F%28-15%2F2%29%2B1%2F9=%281%2F2%29%28-2%2F15%29%2B1%2F9=-1%2F15%2B1%2F9=-3%2F45%2B5%2F45=2%2F45 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "IMPORTANT NOTE:<BR>\n" );
document.write( "The long horizontal bar above <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%5E2%2B20a-80 ALIGN=MIDDLE  ALT=\"10a%5E2%2B20a-80\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a grouping symbol.<BR>\n" );
document.write( "It means that there are understood, invisible parentheses wrapping up, as separate packages,<BR>\n" );
document.write( "what's on top of the line,<BR>\n" );
document.write( "and whats below the line.<BR>\n" );
document.write( "When typing math, you need to type those parentheses,<BR>\n" );
document.write( "as required by the internationally agreed upon order of operations rules.<BR>\n" );
document.write( "If you don't you will not be understood.<BR>\n" );
document.write( "You probably, will get the wrong results,<BR>\n" );
document.write( "and reporting wrong results will get you in trouble.<BR>\n" );
document.write( "(As an analytical chemist, I know that).<BR>\n" );
document.write( "(100-25)/(100+25)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100-25%29%2F%28100%2B25%29=75%2F125=3%2F5=0.6 ALIGN=MIDDLE  ALT=\"%28100-25%29%2F%28100%2B25%29=75%2F125=3%2F5=0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but if you type 100-25/100+25=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100-25%2F100%2B25=100-0.25%2B25=124.75 ALIGN=MIDDLE  ALT=\"100-25%2F100%2B25=100-0.25%2B25=124.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "most calculators will give you the correct answer as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=124.75 ALIGN=MIDDLE  ALT=\"124.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );