SOLUTION: The sum of two numbers is −34. You want to maximize their product. Determine the two numbers m and n using the method of completing the square. Show your work.

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Question 1177207: The sum of two numbers is −34. You want to maximize their product. Determine the two numbers m and n using the method of completing the square. Show your work.

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of two numbers is 34.
x%2By=34
y=34-x
their product:
xy...........substitute y
=x%2834-x%29
=34x-x%5E2............complete square
=-%28x%5E2-34x%2Bb%5E2%29-%28-b%5E2%29........b=34%2F2=17
=-%28x%5E2-34x%2B17%5E2%29%2B17%5E2
=-%28x-17%29%5E2%2B289
=> numbers are: x=17 and+y=17

Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The  "solution"  by  @MathLover1 is irrelevant to the posed problem,  since she solved  DIFFERENT  problem.

            So I came to bring the  TRUE  solution.



The sum of two numbers is -34.
x%2By=-34
y=-34-x

their product:
xy...........substitute y

=x%28-34-x%29
=-34x-x%5E2............complete square
=-%28x%5E2%2B34x%2Bb%5E2%29-%28-b%5E2%29........b=-34%2F2=-17
=-%28x%5E2%2B34x%2B17%5E2%29%2B17%5E2
=-%28x%2B17%29%5E2%2B289

=> the numbers are:   x= -17   and   y= -17.             ANSWER

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Solved.