document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130742>Question 130742</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013062568x/algebrahomeworkh>Algrebra II</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-x%29%5E%281%2F2%29-1=x ALIGN=MIDDLE  ALT=\"%285-x%29%5E%281%2F2%29-1=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95460 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=95460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You don't actually say, but I'll presume that you need to solve this equation for x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-x%29%5E%281%2F2%29-1=x ALIGN=MIDDLE  ALT=\"%285-x%29%5E%281%2F2%29-1=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%281%2F2%29=sqrt%28a%29 ALIGN=MIDDLE  ALT=\"a%5E%281%2F2%29=sqrt%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so your equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285-x%29-1=x ALIGN=MIDDLE  ALT=\"sqrt%285-x%29-1=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 1 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%285-x%29=x%2B1 ALIGN=MIDDLE  ALT=\"sqrt%285-x%29=x%2B1\"   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=5-x=x%5E2%2B2x%2B1 ALIGN=MIDDLE  ALT=\"5-x=x%5E2%2B2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Put the equation in standard form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2-2x-1%2B5-x=0 ALIGN=MIDDLE  ALT=\"-x%5E2-2x-1%2B5-x=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%5E2-3x%2B4=0 ALIGN=MIDDLE  ALT=\"-x%5E2-3x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply by -1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x-4=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x-4=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=4%2A-1=-4 ALIGN=MIDDLE  ALT=\"4%2A-1=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-1=3 ALIGN=MIDDLE  ALT=\"4-1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this quadratic factors to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "Therefore <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;\" >.  However, since this is a radical equation (meaning that the variable is under a radical sign), there is a possibility that by squaring both sides of the equation, we may have derived an equation that is not exactly equivalent to the original and have introduced an extraneous root.\r<BR>\n" );
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document.write( "Check the answers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-1%29%5E%281%2F2%29-1=1 ALIGN=MIDDLE  ALT=\"%285-1%29%5E%281%2F2%29-1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%5E%281%2F2%29-1=1 ALIGN=MIDDLE  ALT=\"%284%29%5E%281%2F2%29-1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-1=1 ALIGN=MIDDLE  ALT=\"2-1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >:  True statement.  <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;\" > is in the solution set.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-%28-4%29%29%5E%281%2F2%29-1=-4 ALIGN=MIDDLE  ALT=\"%285-%28-4%29%29%5E%281%2F2%29-1=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%29%5E%281%2F2%29-1=-4 ALIGN=MIDDLE  ALT=\"%289%29%5E%281%2F2%29-1=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-1=2%3C%3E-4 ALIGN=MIDDLE  ALT=\"3-1=2%3C%3E-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >:  False statement.  <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 NOT in the solution set.\r<BR>\n" );
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document.write( "<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;\" >, and that's my final answer, Regis. </SPAN>\n" );
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