Problem:
The sum of two integers is minus 11 and their product is -80. Find the two integers.

Solution:
To solve this problem, we can use the following steps:

1. Identify the two integers: Let's call the two integers x and y.

2. Write down the given information: We know that x + y = -11 and xy = -80.

3. Solve for one variable in terms of the other: We can use the first equation to solve for one variable in terms of the other. For example, we can solve for x in terms of y as follows:

x + y = -11
x = -y - 11

4. Substitute into the second equation: We can substitute the expression for x into the second equation and solve for y. We get:

(-y - 11)y = -80
-y^2 - 11y + 80 = 0

5. Solve for y: We can solve for y using the quadratic formula:

y = (-(-11) ± sqrt((-11)^2 - 4(-1)(80))) / (2(-1))
y = (-(-11) ± sqrt(121 + 320)) / (-2)
y = (11 ± sqrt(441)) / 2
y = (11 ± 21) / 2

So we get two possible values for y: y = -5 or y = 8.

6. Solve for x: We can use the expression we found for x in step 3 to find the corresponding values of x. If y = -5, we get x = -6. If y = 8, we get x = -3.

Answer:
The two integers are -6 and -5 or -3 and 8.

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