document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=663417>Question 663417</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, this question loses me, I tried setting this up in a y=x^2+z^2 format and substituting but I get lost very quickly.\r<BR>\n" );
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document.write( "QUESTION: \"Find two non-negative numbers whose sum is 18.5 and the sum of their squares is a minimum.\"\r<BR>\n" );
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document.write( "I had<BR>\n" );
document.write( "x^2+(18.5-x)^2<BR>\n" );
document.write( "=x^2+342.25-37x+x^2<BR>\n" );
document.write( "=2x^2-37x+342.25<BR>\n" );
document.write( "and then I got very lost. Someone suggested I used -b/2a to help me solve but I'm not sure what I'm supposed to do.\r<BR>\n" );
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document.write( "Thanks for the help in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #412793 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=412793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose I vary one of the numbers and hold<BR>\n" );
document.write( "the other number fixed, but not saying <BR>\n" );
document.write( "right away what it is fixed at.<BR>\n" );
document.write( "Let the variable number = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let the fixed number = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+a+=+18.5+ ALIGN=MIDDLE  ALT=\"+x+%2B+a+=+18.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+x%5E2+%2B+a%5E2+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E2+%2B+a%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+18.5+-+x++ ALIGN=MIDDLE  ALT=\"+a+=+18.5+-+x++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+x%5E2+%2B+%28+18.5+-+x+%29%5E2+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E2+%2B+%28+18.5+-+x+%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+x%5E2+%2B+342.25+-+37x+%2B+x%5E2+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E2+%2B+342.25+-+37x+%2B+x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+2x%5E2+-+37x+%2B+342.25+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+2x%5E2+-+37x+%2B+342.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( just what you got )<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "This is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ax%5E2+%2B+bx+%2B+c+ ALIGN=MIDDLE  ALT=\"+ax%5E2+%2B+bx+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the <BR>\n" );
document.write( "minimum is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+2+ ALIGN=MIDDLE  ALT=\"+a+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-37+ ALIGN=MIDDLE  ALT=\"+b+=+-37+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+-%28-37%29+%2F+%282%2A2%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-%28-37%29+%2F+%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+37%2F4+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+37%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+37%2F4+=+9.25+ ALIGN=MIDDLE  ALT=\"+37%2F4+=+9.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+18.5+-+x++ ALIGN=MIDDLE  ALT=\"+a+=+18.5+-+x++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+18.5+-+9.25+ ALIGN=MIDDLE  ALT=\"+a+=+18.5+-+9.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+9.25+ ALIGN=MIDDLE  ALT=\"+a+=+9.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both numbers are 9.25<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A9.25%5E2++=+171.125+ ALIGN=MIDDLE  ALT=\"+2%2A9.25%5E2++=+171.125+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "What if the numbers are<BR>\n" );
document.write( "9.24 and 9.26<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9.24%5E2+%2B+9.26%5E2+=+85.3776+%2B+85.7476+ ALIGN=MIDDLE  ALT=\"+9.24%5E2+%2B+9.26%5E2+=+85.3776+%2B+85.7476+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+85.3776+%2B+85.7476+=+171.1252+ ALIGN=MIDDLE  ALT=\"+85.3776+%2B+85.7476+=+171.1252+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is higher than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A9.25%5E2+ ALIGN=MIDDLE  ALT=\"+2%2A9.25%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So we have a minimum<BR>\n" );
document.write( " \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );