Answer:
The two numbers are -18 and 11 or 7 and -14, since the order of the numbers does not matter in finding their product and sum.
Explanation:
Given the product of two numbers is -78 and their sum is -7, we can use algebra to find these two numbers. Let's call these numbers x and y. Then, we have:
x * y = -78
x + y = -7
We can use the second equation to solve for one of the variables and then substitute it into the first equation to find the other variable. For example, solving for x:
x = -7 - y
x * y = -78
(-7 - y) * y = -78
-7y - y^2 = -78
y^2 + 7y + 78 = 0
This is a quadratic equation which can be solved using the quadratic formula or factoring. The two solutions for y are -14 and 11. Then, we can use the second equation to find x:
x = -7 - y
x = -7 - (-14) = 7
x = -7 - 11 = -18
So, the two numbers are -18 and 11 or 7 and -14, since the order of the numbers does not matter in finding their product and sum.