Two numbers have a product of 56 and their sum of -15 what are the numbers?

Answer 1

71

Answer 2

Identify the variables:

x = 1st number

y = 2nd number

Write two equations for them from the worded question:

xy = 56 [1]

x+y = -15 [2]

Rewrite y in terms of x

y = -15-x [3]

Substitute [3] into [1]

x(-15-x) = 56

Expand

-15x-x^2 = 56

Add 15x and x^2 to both sides

x^2+15x+56 = 0

Factorise

(x+7)(x+8) = 0

x = -8 or -7

Substitute x values into 3rd equation for y

When x=-8, y = -15-(-8)

y = -7

When x = -7, y = -15-(-7)

y = -8

So the numbers are either

x = -8, y = -7

OR

x = -7, y = -8