Given that the product of two consecutive numbers is 182.

Let us assume that the first number is x.

Then, the next number will be x+1.

We will rewrite the product of both numbers.

==> x*(x+1) = 182

Let us open the brackets.

==> x^2 + x = 182

==>...

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Given that the product of two consecutive numbers is 182.

Let us assume that the first number is x.

Then, the next number will be x+1.

We will rewrite the product of both numbers.

==> x*(x+1) = 182

Let us open the brackets.

==> x^2 + x = 182

==> x^2 + x - 182 = 0

Now we have a quadratic equation, we will use the formula to find the roots.

==> x1= ( -1 + sqrt(1+4*182) / 2

=(-1 + 27) /2

= 26/2 = 13

==> x1= 13

==> x2= (-1-27)/2 = -28/2 = -14

==> x2= -14

Then the numbers are:

**13 and 14 OR -13 and -14.**