the product of two consecutive, negative integers is 182. what equation represents the situation? what are…

Explanation:

Step1: Let the first negative integer

Let the first negative integer be $x$. Then the next consecutive negative integer is $x + 1$.

Step2: Set up the equation

Since their product is 182, we have the equation $x(x + 1)=182$, which expands to $x^{2}+x - 182=0$.

Step3: Solve the quadratic equation

Factor the quadratic equation: $x^{2}+x - 182=(x + 14)(x - 13)=0$. So $x=-14$ or $x = 13$. But we are looking for negative integers, so we take $x=-14$.

Step4: Find the second number

The second consecutive negative integer is $x + 1=-14 + 1=-13$.

Answer:

The equation is $x(x + 1)=182$ (or $x^{2}+x - 182=0$). The two numbers are -14 and -13.