document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135978>Question 135978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to solve x=&#8730;3x-12 +4   radical sign over 3x-12  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99612 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99612\">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=x=sqrt%283x-12%29%2B4 ALIGN=MIDDLE  ALT=\"x=sqrt%283x-12%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Isolate the radical:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=sqrt%283x-12%29 ALIGN=MIDDLE  ALT=\"x-4=sqrt%283x-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Square both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B16=3x-12 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B16=3x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Put the quadratic in standard form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x-3x%2B16%2B12=0 ALIGN=MIDDLE  ALT=\"x%5E2-8x-3x%2B16%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-11x%2B28=0 ALIGN=MIDDLE  ALT=\"x%5E2-11x%2B28=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2A-4=28 ALIGN=MIDDLE  ALT=\"-7%2A-4=28\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7-4=-11 ALIGN=MIDDLE  ALT=\"-7-4=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this quadratic factors, so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%28x-4%29=0 ALIGN=MIDDLE  ALT=\"%28x-7%29%28x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, by the zero product rule:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-7=0 ALIGN=MIDDLE  ALT=\"x-7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=0 ALIGN=MIDDLE  ALT=\"x-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we had to square both sides of the equation, there is the possibility that we introduced an extraneous root -- one that is a solution to the derived equation but is NOT a solution to the original equation.  Check both answers.\r<BR>\n" );
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document.write( "Is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7=sqrt%283%2A7-12%29%2B4 ALIGN=MIDDLE  ALT=\"7=sqrt%283%2A7-12%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > a true statement?  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2821-12%29%2B4=sqrt%289%29%2B4=3%2B4=7 ALIGN=MIDDLE  ALT=\"sqrt%2821-12%29%2B4=sqrt%289%29%2B4=3%2B4=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Checks, the equation is true when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a valid solution.\r<BR>\n" );
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document.write( "Is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=sqrt%283%2A4-12%29%2B4 ALIGN=MIDDLE  ALT=\"4=sqrt%283%2A4-12%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > a true statement?  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812-12%29%2B4=sqrt%280%29%2B4=0%2B4=0 ALIGN=MIDDLE  ALT=\"sqrt%2812-12%29%2B4=sqrt%280%29%2B4=0%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Checks, the equation is true when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a valid solution.\r<BR>\n" );
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document.write( "No extraneous roots were introduced, so both solutions are valid. </SPAN>\n" );
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