SOLUTION: The sum of two number is 7 and the product is negative 60

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Question 1086882: The sum of two number is 7 and the product is negative 60
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let's two numbers be x and y
if the sum of two number is 7, we have
x%2By=7...solve for x
x=7-y....eq.1
and, if the product is -60, we have
x%2Ay=-60...solve for x
x=-60%2Fy....eq.2
from eq.1 and eq.2 we have

7-y=-60%2Fy
7y-y%5E2=-60
y%5E2-7y-60=0....factor
y%5E2-12y%2B5y-60=0
%28y%5E2-12y%29%2B%285y-60%29=0
y%28y-12%29%2B5%28y-12%29=0
%28y+-+12%29%28y+%2B+5%29+=+0
solutions:
%28y+-+12%29+=+0=>y=12
%28y+%2B+5%29+=+0=>y=-5
now find x:
x=7-y....eq.1...if y=12
x=7-12
x=-5
x=7-y....eq.1...if y=-5
x=7-%28-5%29
x=7%2B5
x=12
so, you can choose x=-5 and y=12 or x=12 and y=-5