document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118200>Question 118200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm trying to solve the following equation:<BR>\n" );
document.write( "The square root of [x+10] plus the square root of [x-6] equals 8.<BR>\n" );
document.write( "I tried squaring both sides, and that eliminates some radicals, but it also creates some more! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86301 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=86301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B10%29+%2B+sqrt%28x-6%29+=+8 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B10%29+%2B+sqrt%28x-6%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "If you have two radicals involved, it often simplifies things to have one radical on one side<BR>\n" );
document.write( "of the equal sign and the other radical on the other side. So let's begin by subtracting<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-6%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides. When you do that the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x+%2B+10%29+=+8+-+sqrt%28x-6%29 ALIGN=MIDDLE  ALT=\"sqrt%28x+%2B+10%29+=+8+-+sqrt%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now square both sides. The left side becomes just x + 10. And on the right side you multiply:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288+-+sqrt%28x-6%29%29%2A%288+-+sqrt%28x+-+6%29%29 ALIGN=MIDDLE  ALT=\"%288+-+sqrt%28x-6%29%29%2A%288+-+sqrt%28x+-+6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Without going into the detail of multiplying these two binomials, the product is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+-+16%2Asqrt%28x-6%29+%2B+%28x-6%29 ALIGN=MIDDLE  ALT=\"64+-+16%2Asqrt%28x-6%29+%2B+%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substituting these new left and right sides into the equation results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B10+=+64+-+16%2Asqrt%28x-6%29+%2B+x+-6 ALIGN=MIDDLE  ALT=\"x%2B10+=+64+-+16%2Asqrt%28x-6%29+%2B+x+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract x from both sides of the equation ... which gets rid of the two x terms and leaves:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+64+-+16%2Asqrt%28x-6%29+-6 ALIGN=MIDDLE  ALT=\"10+=+64+-+16%2Asqrt%28x-6%29+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "On the right side combine the +64 and the -6 to make the right side become:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+-16%2Asqrt%28x+-+6%29+%2B+58 ALIGN=MIDDLE  ALT=\"10+=+-16%2Asqrt%28x+-+6%29+%2B+58\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Get rid of the 10 on the left side by subtracting 10 from both sides:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-16%2Asqrt%28x-6%29+%2B+48 ALIGN=MIDDLE  ALT=\"0+=+-16%2Asqrt%28x-6%29+%2B+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Get rid of the radical on the right side by adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Asqrt%28x-6%29 ALIGN=MIDDLE  ALT=\"16%2Asqrt%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides and you <BR>\n" );
document.write( "have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Asqrt%28x-6%29+=+48 ALIGN=MIDDLE  ALT=\"16%2Asqrt%28x-6%29+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Divide both sides by 16 and you reduce the equation to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-6%29+=+3 ALIGN=MIDDLE  ALT=\"sqrt%28x-6%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Square both sides to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+6+=+9 ALIGN=MIDDLE  ALT=\"x+-+6+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Finally, solve for x by adding 6 to both sides to get rid of the -6 on the left side. When<BR>\n" );
document.write( "you do that, you have the answer:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Check this answer by going back to the original equation:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B10%29+%2B+sqrt%28x-6%29+=+8 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B10%29+%2B+sqrt%28x-6%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute 15 for x and it becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2815%2B10%29+%2B+sqrt%2815-6%29+=+8 ALIGN=MIDDLE  ALT=\"sqrt%2815%2B10%29+%2B+sqrt%2815-6%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and this reduces to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29+%2B+sqrt%289%29+=+8 ALIGN=MIDDLE  ALT=\"sqrt%2825%29+%2B+sqrt%289%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Taking the two square roots gives you:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2B+3+=+8 ALIGN=MIDDLE  ALT=\"5+%2B+3+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "That works ... so the answer of y = 15 looks good.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem and how to solve it. Splitting the radicals ...<BR>\n" );
document.write( "one on one side and the other on the other side seemed to help a bit.<BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );