document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=482538>Question 482538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please i need help with this problem: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B4%29%2Bsqrt%28x-4%29=sqrt%282x%2B6%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B4%29%2Bsqrt%28x-4%29=sqrt%282x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "thank you so much for your time!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #330335 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=330335\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B4%29%2Bsqrt%28x-4%29=sqrt%282x%2B6%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B4%29%2Bsqrt%28x-4%29=sqrt%282x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "To solve, square both sides. For the left side this means multiplying:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%2B4%29%2Bsqrt%28x-4%29%29%2A%28sqrt%28x%2B4%29%2Bsqrt%28x-4%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%2B4%29%2Bsqrt%28x-4%29%29%2A%28sqrt%28x%2B4%29%2Bsqrt%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Use the FOIL system. In the two sets of parentheses, multiply FIRST terms, then multiply OUTSIDE terms, then multiply INSIDE terms, and finally multiply LAST terms. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Firsts:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%2B4%29%29%2A%28sqrt%28x%2B4%29%29=+x%2B4 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%2B4%29%29%2A%28sqrt%28x%2B4%29%29=+x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Outsides: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%2B4%29%29%2A%28sqrt%28x-4%29%29+=+sqrt%28x%5E2+-+16%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%2B4%29%29%2A%28sqrt%28x-4%29%29+=+sqrt%28x%5E2+-+16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Insides: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x-4%29%29%2A%28sqrt%28x%2B4%29%29+=+sqrt%28x%5E2+-+16%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28x-4%29%29%2A%28sqrt%28x%2B4%29%29+=+sqrt%28x%5E2+-+16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Finally, Lasts: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x-4%29%29%2A%28sqrt%28x-4%29%29=+x-4 ALIGN=MIDDLE  ALT=\"%28sqrt%28x-4%29%29%2A%28sqrt%28x-4%29%29=+x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Add all these results together and you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4%2Bsqrt%28x%5E2+-+16%29%2Bsqrt%28x%5E2+-+16%29%2Bx-4 ALIGN=MIDDLE  ALT=\"x%2B4%2Bsqrt%28x%5E2+-+16%29%2Bsqrt%28x%5E2+-+16%29%2Bx-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The two terms containing the radicals are identical. Therefore, they can be added and the overall expression becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4%2B2%2Asqrt%28x%5E2+-+16%29%2Bx-4 ALIGN=MIDDLE  ALT=\"x%2B4%2B2%2Asqrt%28x%5E2+-+16%29%2Bx-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that the +4 and the -4 cancel each other out and also the x + x sum to 2x.  Therefore, the left side that we squared simplifies to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+2%2Asqrt%28x%5E2-16%29 ALIGN=MIDDLE  ALT=\"2x+%2B+2%2Asqrt%28x%5E2-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- this is the left side squared<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now let's return to the original equation and square the right side as follows:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x%2B6%29%29%2A%28sqrt%282x%2B6%29%29=+2x%2B6 ALIGN=MIDDLE  ALT=\"%28sqrt%282x%2B6%29%29%2A%28sqrt%282x%2B6%29%29=+2x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <--- this is the right side squared<BR>\n" );
document.write( ".<BR>\n" );
document.write( "And the square of the left side must equal the square of the right side as follows:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+2%2Asqrt%28x%5E2-16%29=2x%2B6 ALIGN=MIDDLE  ALT=\"2x+%2B+2%2Asqrt%28x%5E2-16%29=2x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that a term 2x appears on both sides. Therefore, subtract 2x from both sides and the equation reduces to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%28x%5E2-16%29+=+6 ALIGN=MIDDLE  ALT=\"2%2Asqrt%28x%5E2-16%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Divide both sides by 2 and you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2-16%29+=+3 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2-16%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now get rid of the radical by squaring both sides again and you have<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-16+=+9 ALIGN=MIDDLE  ALT=\"x%5E2-16+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Get rid of the -16 on the left side by adding 16 to both sides and you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+25 ALIGN=MIDDLE  ALT=\"x%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "And finally, solve for x by taking the square root of both sides. The result is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "And that's the answer. You can return to the original equation that you were given to solve and substitute 5 for x to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B4%29%2Bsqrt%28x-4%29=+sqrt%282x%2B6%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B4%29%2Bsqrt%28x-4%29=+sqrt%282x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Letting x = 5 results in this becoming:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%2B4%29%2Bsqrt%285-1%29=+sqrt%28%282%2A5%29%2B6%29 ALIGN=MIDDLE  ALT=\"sqrt%285%2B4%29%2Bsqrt%285-1%29=+sqrt%28%282%2A5%29%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and this simplifies to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29%2Bsqrt%281%29=+sqrt%2816%29 ALIGN=MIDDLE  ALT=\"sqrt%289%29%2Bsqrt%281%29=+sqrt%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and finally our check shows that by taking the square roots of the three numbers:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B1+=+4 ALIGN=MIDDLE  ALT=\"3%2B1+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "which means that if x = 5 the original equation balances. Both sides are equal.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem and how to work it.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );