document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=543047>Question 543047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3+&#8730;z-10=&#8730;z+5\r<BR>\n" );
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document.write( "I need help solving radical equations please </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354739 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=354739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to solve:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+sqrt%28z-10%29+=+sqrt%28z%2B5%29 ALIGN=MIDDLE  ALT=\"3+%2B+sqrt%28z-10%29+=+sqrt%28z%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Square both sides. For the left side this involves multiplying:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283+%2B+sqrt%28z-10%29%29%2A%283+%2B+sqrt%28z-10%29%29 ALIGN=MIDDLE  ALT=\"%283+%2B+sqrt%28z-10%29%29%2A%283+%2B+sqrt%28z-10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and you can do this by the FOIL process to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+%2B+3%2Asqrt%28z-10%29+%2B+3%2Asqrt%28z-10%29+%2B+%28sqrt%28z+-+10%29%29%5E2 ALIGN=MIDDLE  ALT=\"3%5E2+%2B+3%2Asqrt%28z-10%29+%2B+3%2Asqrt%28z-10%29+%2B+%28sqrt%28z+-+10%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To simplify this, note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+=+9 ALIGN=MIDDLE  ALT=\"3%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
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document.write( "Also note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%28z-10%29+%2B+3%2Asqrt%28z-10%29+=+6%2Asqrt%28z-10%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%28z-10%29+%2B+3%2Asqrt%28z-10%29+=+6%2Asqrt%28z-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And finally note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28z+-+10%29%29%5E2+=+z+-+10 ALIGN=MIDDLE  ALT=\"%28sqrt%28z+-+10%29%29%5E2+=+z+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Make these changes and the squared left side becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%2B+6%2Asqrt%28z-10%29+%2B+z+-+10 ALIGN=MIDDLE  ALT=\"9+%2B+6%2Asqrt%28z-10%29+%2B+z+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Squaring the right side results in: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28z%2B5%29%29%5E2+=+z+%2B+5 ALIGN=MIDDLE  ALT=\"%28sqrt%28z%2B5%29%29%5E2+=+z+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So when both sides of this equation are squared the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%2B+6%2Asqrt%28z-10%29+%2B+z+-+10+=+z+%2B+5 ALIGN=MIDDLE  ALT=\"9+%2B+6%2Asqrt%28z-10%29+%2B+z+-+10+=+z+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that you have a +z on the left side and a +z on the right side. Subtracting z from both sides eliminates these two terms and you are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%2B+6%2Asqrt%28z-10%29+-+10+=++5 ALIGN=MIDDLE  ALT=\"9+%2B+6%2Asqrt%28z-10%29+-+10+=++5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the 9 and the -10 on the left side and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%28z-10%29+-+1+=+5 ALIGN=MIDDLE  ALT=\"6%2Asqrt%28z-10%29+-+1+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the -1 on the left side by adding +1 to both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%28z-10%29+=+6 ALIGN=MIDDLE  ALT=\"6%2Asqrt%28z-10%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 6 and the equation is then:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28z-10%29+=+1 ALIGN=MIDDLE  ALT=\"sqrt%28z-10%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now square both sides and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+-+10+=+1 ALIGN=MIDDLE  ALT=\"z+-+10+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally eliminate the -10 on the left side by adding 10 to both sides and the answer you are looking for becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+11 ALIGN=MIDDLE  ALT=\"z+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can check this out by returning to the original equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+sqrt%28z-10%29+=+sqrt%28z%2B5%29 ALIGN=MIDDLE  ALT=\"3+%2B+sqrt%28z-10%29+=+sqrt%28z%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and substituting 11 for z to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+sqrt%2811-10%29+=+sqrt%2811%2B5%29 ALIGN=MIDDLE  ALT=\"3+%2B+sqrt%2811-10%29+=+sqrt%2811%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+sqrt%281%29+=+sqrt%2816%29 ALIGN=MIDDLE  ALT=\"3+%2B+sqrt%281%29+=+sqrt%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and taking the square roots results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+1+=+4 ALIGN=MIDDLE  ALT=\"3+%2B+1+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is obviously true, so the answer z = 11 checks.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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