document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53925>Question 53925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> square root of 2x-1 (-) the square root of x-5 = 3<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #36167 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=36167\">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%282x-1%29-sqrt%28x-5%29=3 ALIGN=MIDDLE  ALT=\"sqrt%282x-1%29-sqrt%28x-5%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x-1%29-sqrt%28x-5%29%2Bsqrt%28x-5%29=sqrt%28x-5%29%2B3 ALIGN=MIDDLE  ALT=\"sqrt%282x-1%29-sqrt%28x-5%29%2Bsqrt%28x-5%29=sqrt%28x-5%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x-1%29=sqrt%28x-5%29%2B3 ALIGN=MIDDLE  ALT=\"sqrt%282x-1%29=sqrt%28x-5%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x-1%29%29%5E2=%28sqrt%28x-5%29%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%282x-1%29%29%5E2=%28sqrt%28x-5%29%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1=%28sqrt%28x-5%29%2B3%29%28sqrt%28x-5%29%2B3%29 ALIGN=MIDDLE  ALT=\"2x-1=%28sqrt%28x-5%29%2B3%29%28sqrt%28x-5%29%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1=%28sqrt%28x-5%29%29%5E2%2B3sqrt%28x-5%29%2B3sqrt%28x-5%29%2B9 ALIGN=MIDDLE  ALT=\"2x-1=%28sqrt%28x-5%29%29%5E2%2B3sqrt%28x-5%29%2B3sqrt%28x-5%29%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1=x-5%2B6sqrt%28x-5%29%2B9 ALIGN=MIDDLE  ALT=\"2x-1=x-5%2B6sqrt%28x-5%29%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-1=x%2B4%2B6sqrt%28x-5%29 ALIGN=MIDDLE  ALT=\"2x-1=x%2B4%2B6sqrt%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-x-1-4=x-x%2B4-4%2B6sqrt%28x-5%29 ALIGN=MIDDLE  ALT=\"2x-x-1-4=x-x%2B4-4%2B6sqrt%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5=6sqrt%28x-5%29 ALIGN=MIDDLE  ALT=\"x-5=6sqrt%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2=%286sqrt%28x-5%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2=%286sqrt%28x-5%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%28x-5%29=%286%29%5E2%2A%28sqrt%28x-5%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-5%29%28x-5%29=%286%29%5E2%2A%28sqrt%28x-5%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x-5x%2B25=36%28x-5%29 ALIGN=MIDDLE  ALT=\"x%5E2-5x-5x%2B25=36%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-10x%2B25=36x-180 ALIGN=MIDDLE  ALT=\"x%5E2-10x%2B25=36x-180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-10x-36x%2B25%2B180=36x-36x-180%2B180 ALIGN=MIDDLE  ALT=\"x%5E2-10x-36x%2B25%2B180=36x-36x-180%2B180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-46x%2B205=0 ALIGN=MIDDLE  ALT=\"x%5E2-46x%2B205=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-41%29%28x-5%29=0 ALIGN=MIDDLE  ALT=\"%28x-41%29%28x-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x-41=0<BR>\n" );
document.write( "x-41+41=0+41<BR>\n" );
document.write( "x=41<BR>\n" );
document.write( "x-5=0<BR>\n" );
document.write( "x-5+5=0+5<BR>\n" );
document.write( "x=5<BR>\n" );
document.write( "It appear that the solutions are x={5,41}.  However, you have to be especially careful to check problems that involve even roots for extraneous (false) solutions.  <BR>\n" );
document.write( "Substitute 5 back into the original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%285%29-1%29-sqrt%28%285%29-5%29=3 ALIGN=MIDDLE  ALT=\"sqrt%282%285%29-1%29-sqrt%28%285%29-5%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810-1%29-sqrt%285-5%29=3 ALIGN=MIDDLE  ALT=\"sqrt%2810-1%29-sqrt%285-5%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29-sqrt%280%29=3 ALIGN=MIDDLE  ALT=\"sqrt%289%29-sqrt%280%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3-0=3<BR>\n" );
document.write( "3=3 (x=5 checks out)<BR>\n" );
document.write( "Substitute 41 back into the original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%2841%29-1%29-sqrt%28%2841%29-5%29=3 ALIGN=MIDDLE  ALT=\"sqrt%282%2841%29-1%29-sqrt%28%2841%29-5%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2882-1%29-sqrt%2841-5%29=3 ALIGN=MIDDLE  ALT=\"sqrt%2882-1%29-sqrt%2841-5%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2881%29-sqrt%2836%29=3 ALIGN=MIDDLE  ALT=\"sqrt%2881%29-sqrt%2836%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "9-6=3<BR>\n" );
document.write( "3=3 (x=41 checks out)<BR>\n" );
document.write( "We can now safely say that x={5,41}<BR>\n" );
document.write( "Happy Calculating!!!!\r<BR>\n" );
document.write( "<BR>\n" );
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