Two consecutive negative integers have a product of 30. what are the integers?

We have two sets of numbers

-6,-5        5,6

Step-by-step explanation:

Consecutive integers are next to each other

x, x+1

Product means multiply

x(x+1) = 30

Distribute

x^2 +x=30

Subtract 30 from each side

x^2 +x-30 = 30-30

x^2+x-30 =0

Factor

What 2 numbers multiply to give us -30 and add to 1

6 * -5 = -30

6-5 = -1

(x+6) (x-5) = 0

Using the zero product property

x+6=0   x-5=0

x=-6     x=5

x+1  is the next number

-6,-5        5,6

We have two sets of numbers

-6,-5        5,6

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