document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=705205>Question 705205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation. Identify any extraneous solutions. a=&#8730;(-2a)\r<BR>\n" );
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document.write( "A. –2 is a solution of the original equation. 0 is an extraneous solution.	\r<BR>\n" );
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document.write( "B. 0 and –2 are solutions of the original equation.	\r<BR>\n" );
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document.write( "C. 0 is a solution of the original equation. –2 is an extraneous solution.	\r<BR>\n" );
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document.write( "D. 2 is a solution of the original equation. 0 is an extraneous solution.	 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434468 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=434468\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The answer is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C%29 ALIGN=MIDDLE  ALT=\"highlight%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. 0 is a solution of the original equation. –2 is an extraneous solution.<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=sqrt%28-2a%29 ALIGN=MIDDLE  ALT=\"a=sqrt%28-2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you square both sides, you get the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=-2a ALIGN=MIDDLE  ALT=\"a%5E2=-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That equation has all the solutions that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=sqrt%28-2a%29 ALIGN=MIDDLE  ALT=\"a=sqrt%28-2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has,<BR>\n" );
document.write( "and then some.<BR>\n" );
document.write( "The solutions for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=-2a ALIGN=MIDDLE  ALT=\"a%5E2=-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-2 ALIGN=MIDDLE  ALT=\"a=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "When we try them on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=sqrt%28-2a%29 ALIGN=MIDDLE  ALT=\"a=sqrt%28-2a%29\"   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=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-2a%29=0 ALIGN=MIDDLE  ALT=\"sqrt%28-2a%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Substituting into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=sqrt%28-2a%29 ALIGN=MIDDLE  ALT=\"a=sqrt%28-2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "that give <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;\" > which verifies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=sqrt%28-2a%29 ALIGN=MIDDLE  ALT=\"a=sqrt%28-2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a solution of the original equation.<BR>\n" );
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document.write( "However, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-2 ALIGN=MIDDLE  ALT=\"a=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-2a%29=sqrt%28-2%28-2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28-2a%29=sqrt%28-2%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-2a%29=sqrt%284%29 ALIGN=MIDDLE  ALT=\"sqrt%28-2a%29=sqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-2a%29=2 ALIGN=MIDDLE  ALT=\"sqrt%28-2a%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-2 ALIGN=MIDDLE  ALT=\"a=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=sqrt%28-2a%29 ALIGN=MIDDLE  ALT=\"a=sqrt%28-2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=2 ALIGN=MIDDLE  ALT=\"-2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is not true.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-2 ALIGN=MIDDLE  ALT=\"a=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an extraneous solution.<BR>\n" );
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