SOLUTION: what multiplies to be -3 but adds to be -5

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Question 1128066: what multiplies to be -3 but adds to be -5
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
xy=-3
x+y=-5
so y=-5-x
substitute
x(-5-x)=-3
-5x-x^2=-3
0=x^2+5x-3
x=(1/2)(-5+/- sqrt (37))
numerically, this is 0.54 for x and -5.54
y would be -5.54 and +0.54 respectively

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

let’s two numbers be x and y

xy=-3 and assuming y%3Ex, y%2Bx=-5.
Two equations and two unknown variables.

y=-5-x from the second equation.
x%28-5-x%29=-3 substituted into the first equation.
-x%5E2-5x=-3
x%5E2%2B5x-3=0..........cannot be factored completely, so use quadratic formula and you will get
x+=+-5%2F2+-+sqrt%2837%29%2F2 or x+=+-5%2F2+%2B+sqrt%2837%29%2F2
then, go to y=-5-x and find y
y=-5-%28-5%2F2+-+sqrt%2837%29%2F2%29
y=-5%2B5%2F2+%2B+sqrt%2837%29%2F2
y=-10%2F2%2B5%2F2+%2B+sqrt%2837%29%2F2
y=-5%2F2+%2B+sqrt%2837%29%2F2 or y=-5%2F2+%2B+sqrt%2837%29%2F2

highlight%28exact%29 solutions are: assuming y%3Ex
x+=+-5%2F2+-+sqrt%2837%29%2F2
y=-5%2F2+%2B+sqrt%2837%29%2F2
check:
%28+-5%2F2+-+sqrt%2837%29%2F2%29%28-5%2F2+%2B+sqrt%2837%29%2F2%29=-3
%28%28+-5+-+sqrt%2837%29%29%28-5%2B+sqrt%2837%29%29%29%2F4=-3
%28%28+-5%29%5E2+-+%28sqrt%2837%29%29%5E2%29%2F4=-3
%2825+-+37%29%2F4=-3
+-+12%2F4=-3
+-+3=-3

%28+-5%2F2+-+sqrt%2837%29%2F2%29%2B%28-5%2F2+%2B+sqrt%2837%29%2F2%29=-5
+-5%2F2+-cross%28+sqrt%2837%29%2F2%29-5%2F2+%2B+cross%28sqrt%2837%29%2F2%29=-5
-5%2F2+-5%2F2+=-5
+-10%2F2+=-5
+-5+=-5