Find a pair of integers with a product of -84 and a sum of 5?

Ah, the search for the elusive integers with a twist! Let me put on my detective glasses and solve this equation mystery for you. Now, we're looking for two integers whose product is -84. To find them, we need to consider all possible pairs that, when multiplied, give us -84.

Now, let's see... -84 can be written as (-1) * 84, or (-2) * 42, or (-3) * 28, and so on. You get the idea. But hold on, we can't forget about the sum of 5! We need to find a pair of integers that also adds up to 5.

After some intense investigation, I've got your answer! The pair of integers that fits the bill is 12 and -7. Why, you ask? Well, 12 * -7 equals -84, and when you add them up, you get 5. Voila! Now we have our mystery-solving, number-crunching duo. Case closed!

To find a pair of integers with a product of -84 and a sum of 5, we can use a method called "factorization."

First, let's list the factors or divisors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. We'll consider both positive and negative factors.

Next, we'll check each pair of factors to see if their sum is equal to 5.

Considering the factors of 84, we find the following pairs with a sum of 5:
-42 + 7 = -35
-21 + 14 = -7
-12 + 21 = 9

Since none of the pairs have a sum of 5, we can modify the problem slightly and allow the product to be either positive or negative. In that case, we can use the factors of 84 and look for pairs with a difference of 5.

Considering the factors of 84, we find the following pairs with a difference of 5:
-42 - (-7) = -35 + 7 = -28
-7 - (-12) = -7 + 12 = 5

So, the pair of integers that have a product of -84 and a sum of 5 is (-7, -12).