document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001292>Question 1001292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which is the extraneous solution of -x = &#8730;2x+15?<BR>\n" );
document.write( "The options are -5, -3, 3, or 5.\r<BR>\n" );
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document.write( "Extraneous solutions are very hard for me to find. Thank you for any help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618529 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=618529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x=sqrt%282x%2B15%29 ALIGN=MIDDLE  ALT=\"-x=sqrt%282x%2B15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be some of the solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%29%5E2=%28sqrt%282x%2B15%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28-x%29%5E2=%28sqrt%282x%2B15%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We solve the second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=2x%2B15 ALIGN=MIDDLE  ALT=\"x%5E2=2x%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x=15 ALIGN=MIDDLE  ALT=\"x%5E2-2x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B1=16 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2=16 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solutions are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=4 ALIGN=MIDDLE  ALT=\"x-1=4\"   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;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=-4 ALIGN=MIDDLE  ALT=\"x-1=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><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;\" > .<BR>\n" );
document.write( "If one of them is not a solution of the original equation,<BR>\n" );
document.write( "that one is an extraneous solution.<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x=sqrt%282x%2B15%29 ALIGN=MIDDLE  ALT=\"-x=sqrt%282x%2B15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > obviously requires a negative <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "it is easy to see that 5 is an extraneous solution.<BR>\n" );
document.write( "You can check and see that <BR>\n" );
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;\" > is a solution to the original equation. </SPAN>\n" );
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