what two numbers can you multiply to get -66 but add to get -7

Answer 1

xy=-66

x+y=-7

y=-7-x

x(-7-x) =-66

x(7+x) = 66

x^2+7x -66 = 0

use the quadratic formula

x = about 5.345

y= about -12.345

is one solution, as xy=5.345(-12.345) = -65.98 which is close to-66

and x+y = 5.345+(-12.345) = -7

more exactly

x=7/2 +/-(1/2)sqr(7^2 +4(66))=(-7+/-sqr313)/2

y = -7-x= -7 -7/2 +/-(1/2)sqr(7^2+4(66))= -7 +/-(-7+/-sqr313)/2

had the problem just been x+y=-5, and xy=-66 then

y=-5-x and

xy = x(-5-x) =-66

x^2 +5x -66=0

(x-6)(x+11) =0

x=6,-11

y=-11, 6

(x,y)= (6,-11) or (-11,6)