document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54627>Question 54627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B7%29+%2B+sqrt%28x%2B2%29+=+sqrt%28x-1%29+-+sqrt%28x-2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B7%29+%2B+sqrt%28x%2B2%29+=+sqrt%28x-1%29+-+sqrt%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "When I solve the above equation, I get x = 2; but when I verify my answer by substituting the value of x in the original equation, it is not matching.  I tried a few times to solve using different methods and I am always getting the same value of x as 2.  What am I doing wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #36895 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=36895\">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%28x%2B7%29+%2B+sqrt%28x%2B2%29+=+sqrt%28x-1%29+-+sqrt%28x-2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B7%29+%2B+sqrt%28x%2B2%29+=+sqrt%28x-1%29+-+sqrt%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Squaring both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%2B7%29+%2B+sqrt%28x%2B2%29%29%5E2+=+%28sqrt%28x-1%29+-+sqrt%28x-2%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%2B7%29+%2B+sqrt%28x%2B2%29%29%5E2+=+%28sqrt%28x-1%29+-+sqrt%28x-2%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%2B7%29%2B%28x%2B2%29+%2B+2%2Asqrt%28x%2B7%29%2Asqrt%28x%2B2%29+=+%28x-1%29+%2B+%28x-2%29+-+2%2Asqrt%28x-1%29%2Asqrt%28x-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+9+%2B+2%2Asqrt%28x%2B7%29%2Asqrt%28x%2B2%29+=+2x+-+3+-+2%2Asqrt%28x-1%29%2Asqrt%28x-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+%2B+2%2Asqrt%28x%2B7%29%2Asqrt%28x%2B2%29+=+-+2%2Asqrt%28x-1%29%2Asqrt%28x-2%29 ALIGN=MIDDLE  ALT=\"12+%2B+2%2Asqrt%28x%2B7%29%2Asqrt%28x%2B2%29+=+-+2%2Asqrt%28x-1%29%2Asqrt%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+-sqrt%28x%2B7%29%2Asqrt%28x%2B2%29+-+sqrt%28x-1%29%2Asqrt%28x-2%29 ALIGN=MIDDLE  ALT=\"6+=+-sqrt%28x%2B7%29%2Asqrt%28x%2B2%29+-+sqrt%28x-1%29%2Asqrt%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Squaring again<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+=+%28x%2B7%29%28x%2B2%29+%2B+%28x-1%29%2A%28x-2%29+%2B+2%2Asqrt%28x%2B7%29%2Asqrt%28x%2B2%29%2Asqrt%28x-1%29%2Asqrt%28x-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+=+x%5E2%2B9x%2B14+%2B+x%5E2-3x%2B2+%2B+2%2Asqrt%28x%2B7%29%2Asqrt%28x%2B2%29%2Asqrt%28x-1%29%2Asqrt%28x-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+=+2x%5E2%2B6x%2B16+%2B+2%2Asqrt%28x%2B7%29%2Asqrt%28x%2B2%29%2Asqrt%28x-1%29%2Asqrt%28x-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+x%5E2%2B3x+%2B+sqrt%28x%2B7%29%2Asqrt%28x%2B2%29%2Asqrt%28x-1%29%2Asqrt%28x-2%29 ALIGN=MIDDLE  ALT=\"10+=+x%5E2%2B3x+%2B+sqrt%28x%2B7%29%2Asqrt%28x%2B2%29%2Asqrt%28x-1%29%2Asqrt%28x-2%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+-+3x+-+10=+-sqrt%28x%2B7%29%2Asqrt%28x%2B2%29%2Asqrt%28x-1%29%2Asqrt%28x-2%29 ALIGN=MIDDLE  ALT=\"x%5E2+-+3x+-+10=+-sqrt%28x%2B7%29%2Asqrt%28x%2B2%29%2Asqrt%28x-1%29%2Asqrt%28x-2%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%2B2%29%28x-5%29+=+-sqrt%28x%2B7%29%2Asqrt%28x%2B2%29%2Asqrt%28x-1%29%2Asqrt%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x-5%29+=+-sqrt%28x%2B7%29%2Asqrt%28x%2B2%29%2Asqrt%28x-1%29%2Asqrt%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Squaring again<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2%28x-5%29%5E2+=+%28x%2B7%29%28x%2B2%29%28x-1%29%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%28x-5%29%5E2+=+%28x%2B7%29%28x%2B2%29%28x-1%29%28x-2%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%2B2%29%28%28x%2B2%29%28x-5%29%5E2+-+%28x%2B7%29%28x-1%29%28x-2%29%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28%28x%2B2%29%28x-5%29%5E2+-+%28x%2B7%29%28x-1%29%28x-2%29%29+=+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%2B2%29%28%28x%2B2%29%28x%5E2+%2B+10x+%2B+25%29+-+%28x%5E2%2B6x-7%29%28x-2%29%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28%28x%2B2%29%28x%5E2+%2B+10x+%2B+25%29+-+%28x%5E2%2B6x-7%29%28x-2%29%29+=+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%2B2%29%28x%5E3+%2B+10x%5E2+%2B+25x+%2B+2x%5E2+%2B+20x+%2B+50+-+x%5E3-6x%5E2%2B7x+%2B2x%5E2%2B12x-14%29+=+0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%288x%5E2+%2B+64x+%2B+36%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%288x%5E2+%2B+64x+%2B+36%29+=+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%2B2%29%282x%5E2+%2B+16x+%2B+9%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%282x%5E2+%2B+16x+%2B+9%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Clearly no root of this equation is equal to 2. The roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-16+%2B-+sqrt%28+16%5E2-4%2A2%2A9+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-16+%2B-+sqrt%28+16%5E2-4%2A2%2A9+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > & -2 i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4+%2B-+sqrt%2846%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+-4+%2B-+sqrt%2846%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > & -2.\r<BR>\n" );
document.write( "\n" );
document.write( "So all values of the x are negative. So the given equation is no longer valid in real domain.\r<BR>\n" );
document.write( "\n" );
document.write( "Note that the equation is satisfied by x=2 if it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B7%29+-+sqrt%28x%2B2%29=... ALIGN=MIDDLE  ALT=\"sqrt%28x%2B7%29+-+sqrt%28x%2B2%29=...\"   DISABLED_style= \"max-width:90%; height:auto;\" > and not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B7%29+%2B+sqrt%28x%2B2%29=... ALIGN=MIDDLE  ALT=\"sqrt%28x%2B7%29+%2B+sqrt%28x%2B2%29=...\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );