What two numbers multiply to equal 36 but also add to equal -6

Answer 1

xy = 36

x+y = -6

y =-6-x

x(-6-x) = 36

-6x -x^2 = 36

x^2 +6x = -36

x^2 +6x + 9 = -36+9 =-27

x+3 = sqr(-27) = isqr27

x =-3 + or - 3isqr3

y=-6-x = 3 + or -3isqr3

graph the two equations, xy=36 and x+y=-6. They never intersect. the only numbers that satisfy those two equations are imaginary. xy=36 is a hyperbola with 2 branches in quadrants I and III. x+y=-6 is a downward sloping line never in quadrant I, but passing through quadrant III, but always above that lower hyperbola branch.

there's a possibility you miscopied the problem, or there's a typo. if 36 were a smaller number there could be a real solution. That seems likely. Or alternatively, if -6 had been a smaller number. for example, If the sum had been -15

then if xy =36 and x+y=-15 then the two numbers would be -3 and -12 they multiply to 36 and sum to -15

Answer 2

x + y = -6. y = - x - 6

xy = 36

x(-x - 6) = 36

-x² - 6x = 36

x² + 6x + 36 = 0

By quadratic formula, x = (-6 ± √(36 - 144)) / 2 = - 3 ± √-108 / 2 = -3 ± 3√3i

Answer 3

x + y = -6

y = -6 - x

xy = 36

x(-6 - x) = 36

-6x - x² = 36

Can you solve for x and answer?