The product of two consecutive negative odd integers is 35. Find the integers.
Let x be the first odd integer. Then the next consecutive odd integer would be x + 2. We know that their product is 35, so:
x(x + 2) = 35
Expanding the expression, we get:
x² + 2x = 35
Rearranging and simplifying:
x² + 2x - 35 = 0
We can factor this quadratic equation to get:
(x + 7)(x - 5) = 0
The two possible solutions are:
x = -7 or x = 5
However, we are only interested in the negative odd integer, so our answer is:
x = -7
Therefore, the two consecutive negative odd integers are -7 and -5.