document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=624779>Question 624779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve for x: 4x(x-5)-5x(x-4)=-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #393054 by </B><A HREF=/tutors/aboutme.mpl?userid=reynard2007><B>reynard2007(52)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reynard2007><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=reynard2007><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=393054\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how I did it:\r<BR>\n" );
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document.write( "<font  DISABLED_style=  arial><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%28x-5%29++-++5x%28x-4%29+=+-1 ALIGN=MIDDLE  ALT=\"4x%28x-5%29++-++5x%28x-4%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >          This is given\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-20x+-+5x%5E2%2B20x=-1 ALIGN=MIDDLE  ALT=\"4x%5E2-20x+-+5x%5E2%2B20x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >            Distribute 4x and -5x to the contents of the parenthesis next to them. DPMA?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2=-1 ALIGN=MIDDLE  ALT=\"-x%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >    Add like terms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B-5x%5E2 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20x%2B20x ALIGN=MIDDLE  ALT=\"-20x%2B20x\"   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%2B1=0 ALIGN=MIDDLE  ALT=\"-x%5E2%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Transpose -1 to the other side of the equation, which makes it positive<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-1=0 ALIGN=MIDDLE  ALT=\"x%5E2-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >    In solving equations like this, oyu are allowed to multiply a number to both sides of the equation, so long as you do it for both sides of the equation. Here, multiply -1 to both sides turning <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2 ALIGN=MIDDLE  ALT=\"-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to positive <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B1 ALIGN=MIDDLE  ALT=\"%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you are familiar with the special product called DOTS <I>(Difference of two squares)</I> this will make solving the equation easier. Given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-1=0 ALIGN=MIDDLE  ALT=\"x%5E2-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > you can factor it to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Equate both of these to 0 and you get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=0 ALIGN=MIDDLE  ALT=\"x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=0 ALIGN=MIDDLE  ALT=\"x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I can't find a way to reply to your comment so, I just edited this.<BR>\n" );
document.write( "when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   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=4%2A%281%29%2A%28%281%29-5%29++-++5%2A%281%29%2A%28%281%29-4%29+=+-1 ALIGN=MIDDLE  ALT=\"4%2A%281%29%2A%28%281%29-5%29++-++5%2A%281%29%2A%28%281%29-4%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%28-4%29-5%2A%28-3%29=-1 ALIGN=MIDDLE  ALT=\"4%2A%28-4%29-5%2A%28-3%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16-%28-15%29=-16%2B15=-1 ALIGN=MIDDLE  ALT=\"-16-%28-15%29=-16%2B15=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can try the same with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hope this does it for your problem.\r<BR>\n" );
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