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

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) (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

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
RELATED QUESTIONS
I am having difficulty understanding how to set up and solve this word problem. My... (answered by scott8148)

Write a word problem that could be solved using the equation... (answered by josgarithmetic)

a) Write a quadratic equation that can be solved by factoring and does not require the... (answered by josgarithmetic,ikleyn)

Can someone please help me with this problem? I am stumped! This is the problem:... (answered by venugopalramana)

Creating my own quadratic equation that cannot be solved by factoring, but can be solved... (answered by stanbon)

I am working on a quadratic equation. A=3, B=6, C=-4. I have worked the problem out to... (answered by nerdybill)

How do you change a problem such as, 2x^2=-6+8x, into a quadratic equation that can be... (answered by nerdybill,stanbon)

My son has to write a word problem that can be solved using a system of linear equations... (answered by stanbon)

Please show me how to solve a quadratic equation using the quadratic formula. Can you... (answered by solver91311)