document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=916040>Question 916040</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: sqrt(2x+3)-sqrt(x+1)=1\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #555903 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=555903\">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%2B3%29-sqrt%28x%2B1%29=1 ALIGN=MIDDLE  ALT=\"sqrt%282x%2B3%29-sqrt%28x%2B1%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1.  Isolate one of the square roots by subtracting the other from both sides.  In this case, I will add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%28x%2B1%29 ALIGN=MIDDLE  ALT=\"-sqrt%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides, giving us\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x%2B3%29=1%2Bsqrt%28x%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%282x%2B3%29=1%2Bsqrt%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2.  Square both sides so that we eliminate the root on the left side.  This will give us\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3=1%2B2%2Asqrt%28x%2B1%29%2Bx%2B1 ALIGN=MIDDLE  ALT=\"2x%2B3=1%2B2%2Asqrt%28x%2B1%29%2Bx%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3.  Combine like terms on the right side, giving us\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3=2%2B2%2Asqrt%28x%2B1%29%2Bx ALIGN=MIDDLE  ALT=\"2x%2B3=2%2B2%2Asqrt%28x%2B1%29%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4.  Subtract the 2 on the right side from both sides of the equal sign, which gives us\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3-2=2%2Asqrt%28x%2B1%29%2Bx ALIGN=MIDDLE  ALT=\"2x%2B3-2=2%2Asqrt%28x%2B1%29%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1=2%2Asqrt%28x%2B1%29%2Bx ALIGN=MIDDLE  ALT=\"2x%2B1=2%2Asqrt%28x%2B1%29%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5.  Subtract the x on the right side from both sides of the equal sign, which gives us\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1-x=2%2Asqrt%28x%2B1%29 ALIGN=MIDDLE  ALT=\"2x%2B1-x=2%2Asqrt%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=2%2Asqrt%28x%2B1%29 ALIGN=MIDDLE  ALT=\"x%2B1=2%2Asqrt%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "6.  Divide both sides of the equation by 2, giving us\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2F2=sqrt%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2F2=sqrt%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "7.  Square both sides of the equal sign to eliminate the radical on the right side, giving us\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B2x%2B1%29%2F4=x%2B1 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B2x%2B1%29%2F4=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8.  Multiply both sides of the equal sign by 4 to get rid of the fraction on the left side, giving us:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B1=4x%2B4 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1=4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "9.  Place all terms on the left side of the equation and set the equation equal to zero:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-4x%2B1-4=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-4x%2B1-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-3=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "10.  Factor the left side of the equation, which will give us\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x-3%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "11.  Set each factor equal to 0 and solve for x for both factors:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=0 ALIGN=MIDDLE  ALT=\"x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >and<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;\" >-----><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=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "12.  Verify that both of these values of x work, by plugging them into the original equation and making sure when plugged in, they equal 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Final Answer:  x = -1 , 3 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );