SOLUTION: 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. QUESTION: "Find two non-negative numbers whose sum is

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.
QUESTION: "Find two non-negative numbers whose sum is 18.5 and the sum of their squares is a minimum."
I had
x^2+(18.5-x)^2
=x^2+342.25-37x+x^2
=2x^2-37x+342.25
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.
Thanks for the help in advance!
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) (Show Source): 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."
I had
x^2+(18.5-x)^2
=x^2+342.25-37x+x^2
=2x^2-37x+342.25
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.
-------------------------------
f(x) = 2x^2-37x+342.25
The min is the vertex of the parabola, at x = -b/2a
x = -(-37)/4 = 9.25
f(9.25) is the minimum
= 171.25
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Suppose I vary one of the numbers and hold
the other number fixed, but not saying
right away what it is fixed at.
Let the variable number =
Let the fixed number =
given:

--------------------

( just what you got )
-----------------------------
This is in the form , so the
minimum is at

and

Both numbers are 9.25
check:

-----------------------
What if the numbers are
9.24 and 9.26

This is higher than
So we have a minimum

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