SOLUTION: My professor says that the following word problem can be solved using a form of the quadratic equation. I can't see it, and all my attempts to solve via trial and error have failed

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: My professor says that the following word problem can be solved using a form of the quadratic equation. I can't see it, and all my attempts to solve via trial and error have failed      Log On


   

Question 84185This question is from textbook Intermediate Algebra
: My professor says that the following word problem can be solved using a form of the quadratic equation. I can't see it, and all my attempts to solve via trial and error have failed. Please explain how this works!
"Find two numbers whose sum is 6 and whose product is 2"
Thanks,
para.lax This question is from textbook Intermediate Algebra

Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=6, x=6-y
x*y=2 now substitute (6-y) for x & solve for y
(6-y)y=2
6y-y^2-2=0
y^2-6y+2=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y=(6+-sqrt[-6^2-4*1*2])/2*1
y=(6+-sqrt36-8])/2
y=(6+-sqrt28)/2
y=(6+-5.29)/2
y=(6+5.29)/2
y=11.29/2
y=5.645 answer. when x=.355.
y=(6-5.29)/2
y=.71/2
y=.355 answer. when x=5.645.
proof
5.645+.355=6
6=6
5.645*.355=2
2=2