document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78786>Question 78786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> square root of x+40-(minus)sqrare root of x =4\r<BR>\n" );
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document.write( "square root of y+10-(minus) square root of y-2 =2\r<BR>\n" );
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document.write( "thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56536 by </B><A HREF=/tutors/aboutme.mpl?userid=mathdoc314><B>mathdoc314(58)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathdoc314><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=56536\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is two problems.  Please ask the second problem separately or work it yourself after you see the technique.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28x%2B40%29+-+sqrt%28x%29+=+4+ ALIGN=MIDDLE  ALT=\"+sqrt%28x%2B40%29+-+sqrt%28x%29+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To solve algebraically, it's necessary to get rid of the square roots in the expression.  I tried to do this with tricks like: rewrite it with\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+%28x%2B20%29+%2B+20+%29+-+sqrt%28+%28x%2B20%29+-+20+%29+=+4+ ALIGN=MIDDLE  ALT=\"+sqrt%28+%28x%2B20%29+%2B+20+%29+-+sqrt%28+%28x%2B20%29+-+20+%29+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "but this did not seem to simplify very well.  So I tried this instead and it worked.  \r<BR>\n" );
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document.write( "Let a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28x%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28x%2B40%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28x%2B40%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(I did this so a will be smaller than b)\r<BR>\n" );
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document.write( "Then solve for a and b like this\r<BR>\n" );
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document.write( "a^2 = x<BR>\n" );
document.write( "b^2 = x + 40 <BR>\n" );
document.write( "therefore b^2 = a^2 + 40.\r<BR>\n" );
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document.write( "The problem stated <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+%28x%2B20%29+%2B+20+%29+-+sqrt%28+%28x%2B20%29+-+20+%29+=+4+ ALIGN=MIDDLE  ALT=\"+sqrt%28+%28x%2B20%29+%2B+20+%29+-+sqrt%28+%28x%2B20%29+-+20+%29+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which now is: b - a = 4.\r<BR>\n" );
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document.write( "b^2 = a^2 + 40<BR>\n" );
document.write( "b - a = 4\r<BR>\n" );
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document.write( "Substitute in for a:<BR>\n" );
document.write( "a = b - 4<BR>\n" );
document.write( "b^2 = (b-4)^2 + 40<BR>\n" );
document.write( "b^2 = (b^2 - 8 b + 16) + 40<BR>\n" );
document.write( "The b^2 cancels out on both sides<BR>\n" );
document.write( "0 = -8 b + 56<BR>\n" );
document.write( "8b = 56<BR>\n" );
document.write( "b = 7<BR>\n" );
document.write( "a = b-4 = 7-4 = 3\r<BR>\n" );
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document.write( "Don't forget to find x<BR>\n" );
document.write( "Evaluate it twice to show it's right:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28x%29+=+3+ ALIGN=MIDDLE  ALT=\"+sqrt%28x%29+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+9+ ALIGN=MIDDLE  ALT=\"+x+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28x-40%29+=+7 ALIGN=MIDDLE  ALT=\"+sqrt%28x-40%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x-40+=+49 ALIGN=MIDDLE  ALT=\"+x-40+=+49\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=9++ ALIGN=MIDDLE  ALT=\"+x=9++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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