document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=26985>Question 26985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E%283%2F2%29-15%28x-3%29%5E%28-1%2F2%29%2B2%28x-3%29%5E%281%2F2%29=0 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E%283%2F2%29-15%28x-3%29%5E%28-1%2F2%29%2B2%28x-3%29%5E%281%2F2%29=0\"   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 #14682 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=14682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK, as it stands it looks too complicated to solve. However, i notice a repeating expression in all three terms, namely <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E%283%2F2%29-15%28x-3%29%5E%28-1%2F2%29%2B2%28x-3%29%5E%281%2F2%29=0 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E%283%2F2%29-15%28x-3%29%5E%28-1%2F2%29%2B2%28x-3%29%5E%281%2F2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28x-3%29%5E%281%2F2%29%29%5E3+-+15%28%28x-3%29%5E%281%2F2%29%29%5E%28-1%29+%2B+2%28x-3%29%5E%281%2F2%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > which is then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E3+-+15y%5E%28-1%29+%2B+2y+=+0 ALIGN=MIDDLE  ALT=\"+y%5E3+-+15y%5E%28-1%29+%2B+2y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Instantly, this is far simpler to look at and approach.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E3+-+%2815%2Fy%29+%2B+2y+=+0 ALIGN=MIDDLE  ALT=\"+y%5E3+-+%2815%2Fy%29+%2B+2y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E4+-+15+%2B+2y%5E2+=+0 ALIGN=MIDDLE  ALT=\"+y%5E4+-+15+%2B+2y%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E4+%2B+2y%5E2+-15+=+0 ALIGN=MIDDLE  ALT=\"+y%5E4+%2B+2y%5E2+-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=+%28y%5E2+-+3%29%28y%5E2+%2B+5%29+=+0 ALIGN=MIDDLE  ALT=\"+%28y%5E2+-+3%29%28y%5E2+%2B+5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2+-+3%29+=+0 ALIGN=MIDDLE  ALT=\"%28y%5E2+-+3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2+%2B+5%29+=+0 ALIGN=MIDDLE  ALT=\"%28y%5E2+%2B+5%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=y%5E2+=+3 ALIGN=MIDDLE  ALT=\"y%5E2+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+-5 ALIGN=MIDDLE  ALT=\"y%5E2+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%283%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-sqrt%283%29 ALIGN=MIDDLE  ALT=\"y+=+-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28-5%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-sqrt%28-5%29 ALIGN=MIDDLE  ALT=\"y+=+-sqrt%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, we have 4 answers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%283%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-sqrt%283%29 ALIGN=MIDDLE  ALT=\"y+=+-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28-5%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-sqrt%28-5%29 ALIGN=MIDDLE  ALT=\"y+=+-sqrt%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, we have to find what x is, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-3%29%5E%281%2F2%29+=+sqrt%283%29+ ALIGN=MIDDLE  ALT=\"+%28x-3%29%5E%281%2F2%29+=+sqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> (x-3) = 3<BR>\n" );
document.write( "--> x = 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-3%29%5E%281%2F2%29+=+-sqrt%283%29+ ALIGN=MIDDLE  ALT=\"+%28x-3%29%5E%281%2F2%29+=+-sqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> (x-3) = 3<BR>\n" );
document.write( "--> x = 6 again.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-3%29%5E%281%2F2%29+=+sqrt%28-5%29+ ALIGN=MIDDLE  ALT=\"+%28x-3%29%5E%281%2F2%29+=+sqrt%28-5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> (x-3) = -5<BR>\n" );
document.write( "--> x = -2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-3%29%5E%281%2F2%29+=+-sqrt%28-5%29+ ALIGN=MIDDLE  ALT=\"+%28x-3%29%5E%281%2F2%29+=+-sqrt%28-5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> (x-3) = -5<BR>\n" );
document.write( "--> x = -2\r<BR>\n" );
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document.write( "So, the 2 answers are x=-2 and x=6\r<BR>\n" );
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document.write( "I would suggest you put both values back into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E%283%2F2%29-15%28x-3%29%5E%28-1%2F2%29%2B2%28x-3%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E%283%2F2%29-15%28x-3%29%5E%28-1%2F2%29%2B2%28x-3%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to make sure that it does indeed equal zero.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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