document.write( "Question 663417: 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
\n" ); document.write( "\n" ); document.write( "QUESTION: \"Find two non-negative numbers whose sum is 18.5 and the sum of their squares is a minimum.\"\r
\n" ); document.write( "\n" ); document.write( "I had
\n" ); document.write( "x^2+(18.5-x)^2
\n" ); document.write( "=x^2+342.25-37x+x^2
\n" ); document.write( "=2x^2-37x+342.25
\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
\n" ); document.write( "\n" ); document.write( "Thanks for the help in advance! \n" ); document.write( "

Algebra.Com's Answer #412771 by Alan3354(69443) $\"\"$ $\"About$

You can put this solution on YOUR website!
QUESTION: \"Find two non-negative numbers whose sum is 18.5 and the sum of their squares is a minimum.\"\r
\n" ); document.write( "\n" ); document.write( "I had
\n" ); document.write( "x^2+(18.5-x)^2
\n" ); document.write( "=x^2+342.25-37x+x^2
\n" ); document.write( "=2x^2-37x+342.25
\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.
\n" ); document.write( "-------------------------------
\n" ); document.write( "f(x) = 2x^2-37x+342.25
\n" ); document.write( "The min is the vertex of the parabola, at x = -b/2a
\n" ); document.write( "x = -(-37)/4 = 9.25
\n" ); document.write( "f(9.25) is the minimum
\n" ); document.write( "= 171.25 \n" ); document.write( "

\n" );