document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=742097>Question 742097</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286x%2B7%29-sqrt%283x%2B3%29=1 ALIGN=MIDDLE  ALT=\"sqrt%286x%2B7%29-sqrt%283x%2B3%29=1\"   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 #452307 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=452307\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Having 2 square roots in an equation, make it a little more complicated to solve than an equation with just one square root.<BR>\n" );
document.write( "As for the simpler equations with square roots, you would square both sides of an equal sign; find solutions to the new equation, and then check those solutions against the original equation.<BR>\n" );
document.write( "However, the arithmetic is usually easier if you start with one square root on each side of the equal sign, so the recommended first step (before the squaring) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286x%2B7%29-sqrt%283x%2B3%29=1 ALIGN=MIDDLE  ALT=\"sqrt%286x%2B7%29-sqrt%283x%2B3%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286x%2B7%29=sqrt%283x%2B3%29%2B1 ALIGN=MIDDLE  ALT=\"sqrt%286x%2B7%29=sqrt%283x%2B3%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "FINDING POSSIBLE SOLUTIONS:<BR>\n" );
document.write( "Then, we square both sides to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B7=3x%2B3%2B1%2B2sqrt%283x%2B3%29 ALIGN=MIDDLE  ALT=\"6x%2B7=3x%2B3%2B1%2B2sqrt%283x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B3=2sqrt%283x%2B3%29 ALIGN=MIDDLE  ALT=\"3x%2B3=2sqrt%283x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At this point we can square again and keep chugging along, to get to the solutions.<BR>\n" );
document.write( "Alternatively, if we define <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%283x%2B3%29 ALIGN=MIDDLE  ALT=\"y=sqrt%283x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the equation above can be written as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=2y ALIGN=MIDDLE  ALT=\"y%5E2=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-2y=0 ALIGN=MIDDLE  ALT=\"y%5E2-2y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28y-2%29=0 ALIGN=MIDDLE  ALT=\"y%28y-2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "with solutions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which mean<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%2B3%29=0 ALIGN=MIDDLE  ALT=\"sqrt%283x%2B3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B3=0 ALIGN=MIDDLE  ALT=\"3x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-3 ALIGN=MIDDLE  ALT=\"3x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <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<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%2B3%29=2 ALIGN=MIDDLE  ALT=\"sqrt%283x%2B3%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B3=4 ALIGN=MIDDLE  ALT=\"3x%2B3=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=1 ALIGN=MIDDLE  ALT=\"3x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F3 ALIGN=MIDDLE  ALT=\"x=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Any way we get to them, our possible solutions are <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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F3 ALIGN=MIDDLE  ALT=\"x=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "CHECKING:<BR>\n" );
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;\" > makes the original equation true:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286x%2B7%29-sqrt%283x%2B3%29=sqrt%28-6%2B7%29-sqrt%28-3%2B3%29=sqrt%281%29-sqrt%280%29=1-0=1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a solution.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F3 ALIGN=MIDDLE  ALT=\"x=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > also makes the original equation true:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286x%2B7%29-sqrt%283x%2B3%29=sqrt%286%281%2F3%29%2B7%29-sqrt%283%281%2F3%29%2B3%29=sqrt%282%2B7%29-sqrt%281%2B3%29=sqrt%289%29-sqrt%284%29=3-2=1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=1%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=1%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is also a solution. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );