document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172938>Question 172938</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321269470/algebrahomeworkh>Introductory Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation\r<BR>\n" );
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document.write( "sqrt (10 + x) = -1 - sqrt (11 - 5x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127831 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=127831\">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=sqrt+%2810+%2B+x%29+=+-1+-+sqrt+%2811+-+5x%29 ALIGN=MIDDLE  ALT=\"sqrt+%2810+%2B+x%29+=+-1+-+sqrt+%2811+-+5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Square both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Bx=1%2B2sqrt%2811-5x%29%2B11-5x ALIGN=MIDDLE  ALT=\"10%2Bx=1%2B2sqrt%2811-5x%29%2B11-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Collect like terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2B6x=2sqrt%2811-5x%29 ALIGN=MIDDLE  ALT=\"-2%2B6x=2sqrt%2811-5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Square both sides again:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-24x-36x%5E2=4%2811-5x%29 ALIGN=MIDDLE  ALT=\"4-24x-36x%5E2=4%2811-5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Collect like terms and put into standard form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E2-24x-40=0 ALIGN=MIDDLE  ALT=\"36x%5E2-24x-40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve the quadratic:\r<BR>\n" );
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document.write( "In fact, this horror actually factors <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836x-40%29%28x%2B1%29=0 ALIGN=MIDDLE  ALT=\"%2836x-40%29%28x%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10%2F9 ALIGN=MIDDLE  ALT=\"x=10%2F9\"   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( "Well, that was tidy.  But there is a big problem.  Neither one of the roots calculated actually satisfies the original equation -- try it for yourself.  This makes sense because how could the positive square root on the left be equal to a clearly negative number on the right?  What happened is that the process of squaring the variable (twice in this case) introduced extraneous roots.  There is no solution to this equation.  </SPAN>\n" );
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