SOLUTION: what two numbers multiple to -1 but add to -6

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Question 963208: what two numbers multiple to -1 but add to -6
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

xy+=+-1
x+%2B+y+=+-6
--------------------------solve the system of equations:

from
x+%2B+y+=+-6=>x=-6-y
go to xy+=+-1, substitute x:
%28-6-y%29y+=+-1....solve for y
-6y-y%5E2+=+-1
0=y%5E2%2B6y+-1..............use quadratic formula

y+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+
y+=+%28-6+%2B-+sqrt%28+36%2B4+%29%29%2F2+
y+=+%28-6+%2B-+sqrt%2840+%29%29%2F2+
y+=+%28-6+%2B-+sqrt%284%2A10+%29%29%2F2+
y+=+%28-cross%286%293+%2B-+cross%282%29sqrt%2810+%29%29%2Fcross%282%29+
y+=+%28-3+%2B-+sqrt%2810+%29%29+
solutions:
y+=+-3+%2B+sqrt%2810+%29+ or y+=+-3+-+sqrt%2810+%29+
go back to x=-6-y, plug in y
x=-6-%28-3+%2B+sqrt%2810+%29%29
x=-6%2B3+-+sqrt%2810+%29
x=-3-+sqrt%2810+%29
or
x=-6-%28-3+-+sqrt%2810+%29%29
x=-6%2B3+%2Bsqrt%2810+%29
x=-3%2Bsqrt%2810+%29
so, solution sets are:
x=-3-+sqrt%2810+%29 and y+=+-3+%2B+sqrt%2810+%29+
or
x=-3%2Bsqrt%2810+%29 and y+=+-3+-+sqrt%2810+%29+