document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175240>Question 175240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve algebraically and check your potential solutions:  squareroot:x+2-x=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130328 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=130328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It really depends on whether you mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2B2-x=0 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2B2-x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x+%2B+2%29+-+x=0 ALIGN=MIDDLE  ALT=\"sqrt%28x+%2B+2%29+-+x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You could also have meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x+%2B+2+-x%29=0 ALIGN=MIDDLE  ALT=\"sqrt%28x+%2B+2+-x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > but that reduces to the absurdity that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29+=0 ALIGN=MIDDLE  ALT=\"sqrt%282%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so I am discounting that possibility.\r<BR>\n" );
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document.write( "Case 1:\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"t=sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+%2B+2+-+t%5E2=0 ALIGN=MIDDLE  ALT=\"t+%2B+2+-+t%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In standard form:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+-+t+-+2+=+0 ALIGN=MIDDLE  ALT=\"t%5E2+-+t+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This factors to:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t+-+2%29%28t+%2B+1%29=0 ALIGN=MIDDLE  ALT=\"%28t+-+2%29%28t+%2B+1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2 ALIGN=MIDDLE  ALT=\"t+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-1 ALIGN=MIDDLE  ALT=\"t+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"t=sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29+=+2 ALIGN=MIDDLE  ALT=\"sqrt%28x%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29+=+-1 ALIGN=MIDDLE  ALT=\"sqrt%28x%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > meaning:\r<BR>\n" );
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document.write( "<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;\" > 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( "However, since we converted to a higher degree equation in order to solve this, we may have introduced an extraneous (and therefore incorrect) root.  Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29+%2B++2+-+4+=+2+%2B+2+-+4+=+0 ALIGN=MIDDLE  ALT=\"sqrt%284%29+%2B++2+-+4+=+2+%2B+2+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Checks.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%29+%2B++2+-+1+=+2+%3C%3E+0 ALIGN=MIDDLE  ALT=\"sqrt%281%29+%2B++2+-+1+=+2+%3C%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Does not check.  Extraneous root.\r<BR>\n" );
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document.write( "Therefore the solution set is <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( "Case 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x+%2B+2%29+-+x=0 ALIGN=MIDDLE  ALT=\"sqrt%28x+%2B+2%29+-+x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x+%2B+2%29+=+x ALIGN=MIDDLE  ALT=\"sqrt%28x+%2B+2%29+=+x\"   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( "Standard Form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+-+2+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+2%29%28x+%2B+1%29=+0 ALIGN=MIDDLE  ALT=\"%28x+-+2%29%28x+%2B+1%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2+ ALIGN=MIDDLE  ALT=\"x+=+2+\"   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( "Again, since we squared both sides in the solution process, we have the possibility of an extraneous root.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282+%2B+2%29+-+2=+2+-+2+=+0 ALIGN=MIDDLE  ALT=\"sqrt%282+%2B+2%29+-+2=+2+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Checks\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1+%2B+2%29+-+%28-1%29+=+1+%2B+1+=+2+%3C%3E+0 ALIGN=MIDDLE  ALT=\"sqrt%28-1+%2B+2%29+-+%28-1%29+=+1+%2B+1+=+2+%3C%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Does not check.  Extraneous root.\r<BR>\n" );
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document.write( "Solution set is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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