document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178968>Question 178968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all real solutions of the following equation.<BR>\n" );
document.write( "(x + 3)5 - 4(x + 3)3 = 0<BR>\n" );
document.write( "x =__  (smallest solution)<BR>\n" );
document.write( "x =___ <BR>\n" );
document.write( "x = ___ (largest solution)\r<BR>\n" );
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document.write( "i cant seem to figure out how to do this! Help! thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133908 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=133908\">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=%28x+%2B+3%29%5E5+-+4%28x+%2B+3%29%5E3+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+3%29%5E5+-+4%28x+%2B+3%29%5E3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=x%2B3 ALIGN=MIDDLE  ALT=\"z=x%2B3\"   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=z%5E5+-+4z%5E3+=+0 ALIGN=MIDDLE  ALT=\"z%5E5+-+4z%5E3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace each \"x+3\" with \"z\".\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3%28z%5E2+-+4%29+=+0 ALIGN=MIDDLE  ALT=\"z%5E3%28z%5E2+-+4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3 ALIGN=MIDDLE  ALT=\"z%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: you can avoid the substitution, but factoring is much easier to see)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3%28z%2B2%29%28z-2%29+=+0 ALIGN=MIDDLE  ALT=\"z%5E3%28z%2B2%29%28z-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2-1 ALIGN=MIDDLE  ALT=\"z%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%2B2%29%28z-2%29 ALIGN=MIDDLE  ALT=\"%28z%2B2%29%28z-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by use of the difference of squares formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3=0 ALIGN=MIDDLE  ALT=\"z%5E3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2B2=0 ALIGN=MIDDLE  ALT=\"z%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-2=0 ALIGN=MIDDLE  ALT=\"z-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set each factor equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=0 ALIGN=MIDDLE  ALT=\"z=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=-2 ALIGN=MIDDLE  ALT=\"z=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2 ALIGN=MIDDLE  ALT=\"z=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for \"z\" in each case\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3=0 ALIGN=MIDDLE  ALT=\"x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3=-2 ALIGN=MIDDLE  ALT=\"x%2B3=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3=2 ALIGN=MIDDLE  ALT=\"x%2B3=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=x%2B3 ALIGN=MIDDLE  ALT=\"z=x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember, we want to solve for \"x\")\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0-3 ALIGN=MIDDLE  ALT=\"x=0-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2-3 ALIGN=MIDDLE  ALT=\"x=-2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2-3 ALIGN=MIDDLE  ALT=\"x=2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3 from both sides (for each equation)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <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;\" > Combine like terms.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <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( "Note: if you plug in any solution into the given equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+3%29%5E5+-+4%28x+%2B+3%29%5E3+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+3%29%5E5+-+4%28x+%2B+3%29%5E3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify, you should get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > . If you do this to all of the solutions, then this will verify the answer. </SPAN>\n" );
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