document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=963997>Question 963997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Under root(x^2+4*x-21) +under root(x^2-x-6)=under root (6*x^2 -5*x-39)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588936 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=588936\">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%5E2%2B4x-21%29+%2Bsqrt%28x%5E2-x-6%29=sqrt%286x%5E2+-5x-39%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2B4x-21%29+%2Bsqrt%28x%5E2-x-6%29=sqrt%286x%5E2+-5x-39%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%2B7%29%28x-3%29%29+%2Bsqrt%28%28x-3%29%28x%2B2%29%29=sqrt%28%286x%2B13%29%28x-3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor out the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-3%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from all terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B7%29+%2Bsqrt%28x%2B2%29=sqrt%286x%2B13%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B7%29+%2Bsqrt%28x%2B2%29=sqrt%286x%2B13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square both sides,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%2B2sqrt%28%28x%2B7%29%28x%2B2%29%29%2B%28x%2B2%29=6x%2B13 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%2B2sqrt%28%28x%2B7%29%28x%2B2%29%29%2B%28x%2B2%29=6x%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B9%2B2sqrt%28%28x%2B7%29%28x%2B2%29%29%2B%28x%2B2%29=6x%2B13 ALIGN=MIDDLE  ALT=\"2x%2B9%2B2sqrt%28%28x%2B7%29%28x%2B2%29%29%2B%28x%2B2%29=6x%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%28%28x%2B7%29%28x%2B2%29%29=4x%2B4 ALIGN=MIDDLE  ALT=\"2sqrt%28%28x%2B7%29%28x%2B2%29%29=4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%28%28x%2B7%29%28x%2B2%29%29=4%28x%2B1%29 ALIGN=MIDDLE  ALT=\"2sqrt%28%28x%2B7%29%28x%2B2%29%29=4%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%2B7%29%28x%2B2%29%29=2%28x%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x%2B7%29%28x%2B2%29%29=2%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square both sides,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%28x%2B2%29=4%28x%5E2%2B2x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%28x%2B2%29=4%28x%5E2%2B2x%2B1%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%2B9x%2B14=4x%5E2%2B8x%2B4 ALIGN=MIDDLE  ALT=\"x%5E2%2B9x%2B14=4x%5E2%2B8x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B9x%2B14=4x%5E2%2B8x%2B4 ALIGN=MIDDLE  ALT=\"3x%5E2%2B9x%2B14=4x%5E2%2B8x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-x-10=0 ALIGN=MIDDLE  ALT=\"3x%5E2-x-10=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-2%29%283x%2B5%29=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%283x%2B5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Remember we factored out the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-3%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > before so that's still part of the solution. <BR>\n" );
document.write( "We only removed it so that the calculation wouldn't be messier.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-3%29%28x-2%29%283x%2B5%29=0 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%29%28x-2%29%283x%2B5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Three possible solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-3%29=0 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%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=x-3=0 ALIGN=MIDDLE  ALT=\"x-3=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=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Verifying,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%5E2%2B4%283%29-21%29+%2Bsqrt%283%5E2-3-6%29=sqrt%286%283%29%5E2+-5%283%29-39%29 ALIGN=MIDDLE  ALT=\"sqrt%283%5E2%2B4%283%29-21%29+%2Bsqrt%283%5E2-3-6%29=sqrt%286%283%29%5E2+-5%283%29-39%29\"   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%2B12-21%29+%2Bsqrt%289-9%29=sqrt%2854+-15-39%29 ALIGN=MIDDLE  ALT=\"sqrt%289%2B12-21%29+%2Bsqrt%289-9%29=sqrt%2854+-15-39%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B0=0 ALIGN=MIDDLE  ALT=\"0%2B0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True, good solution.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2=0 ALIGN=MIDDLE  ALT=\"x-2=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=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Verifying,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%5E2%2B4%282%29+-21%29+%2Bsqrt%28%282%29%5E2-%282%29-6%29=sqrt%286%282%29%5E2+-5%282%29-39%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=sqrt%284%2B8+-21%29+%2Bsqrt%284-2-6%29=sqrt%28+24-5%282%29-39%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2B8+-21%29+%2Bsqrt%284-2-6%29=sqrt%28+24-5%282%29-39%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-9%29+%2Bsqrt%28-4%29=sqrt%28+-25%29 ALIGN=MIDDLE  ALT=\"sqrt%28-9%29+%2Bsqrt%28-4%29=sqrt%28+-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Leads to a negative square root so not a real solution.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B5=0 ALIGN=MIDDLE  ALT=\"3x%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-5 ALIGN=MIDDLE  ALT=\"3x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+%28-5%2F3%29+ ALIGN=MIDDLE  ALT=\"x=+%28-5%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Verifying,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-5%2F3%29%5E2%2B4%28-5%2F3%29-21%29+%2Bsqrt%28%28-5%2F3%29%5E2-%28-5%2F3%29-6%29=sqrt%286%28-5%2F3%29%5E2+-5%28-5%2F3%29-39%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=sqrt%2825%2F9-20%2F3-21%29+%2Bsqrt%2825%2F9%2B5%2F3-6%29=sqrt%2850%2F3%2B25%2F3+-39%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2F9-20%2F3-21%29+%2Bsqrt%2825%2F9%2B5%2F3-6%29=sqrt%2850%2F3%2B25%2F3+-39%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-224%2F9%29+%2Bsqrt%28-14%2F9%29=sqrt%28-14%29 ALIGN=MIDDLE  ALT=\"sqrt%28-224%2F9%29+%2Bsqrt%28-14%2F9%29=sqrt%28-14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Leads to a negative square root so not a real solution.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Only one real solution, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );