The product of two consecutive negative integers is 110. find both numbers.

  -11, -10

Step-by-step explanation:

You can look at the number 110 and see that it is the product of 10 and 11. The opposites of these numbers are the ones you're looking for:

  -11 and -10

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For numbers close together, their geometric mean is close to their arithmetic mean. That is, you can find the average of the two numbers of interest by looking at the square root of 110.

  √110 ≈ 10.5

so the magnitudes of the consecutive integers of interest are 10 and 11. We want negative values, so those will be ...

  -11 and -10

Conventionally, you would solve this by assigning a variable to one of the numbers and writing the quadratic equation ...

  x(x+1) = 110

Its solution can be by a variety of means, one of which is factoring:

  x² +x -110 = 0

  (x +11)(x -10) = 0

  x = -11 or +10 . . . . . . x = -11 is the solution we want; then x+1 = -10.