two negative integers are 5 units apart on the number line, and their product is 126. what is the sum of the…

Explanation:

Step1: Let the two negative integers

Let one integer be $x$, then the other is $x + 5$ (since they are 5 units apart). Their product is 126, so $x(x + 5)=126$.

Step2: Expand the equation

Expand $x(x + 5)=126$ to get $x^{2}+5x - 126=0$.

Step3: Factor the quadratic equation

Factor $x^{2}+5x - 126=0$ as $(x + 14)(x - 9)=0$.

Step4: Solve for x

Set each factor equal to zero: $x+14 = 0$ gives $x=-14$ and $x - 9=0$ gives $x = 9$. Since we are looking for negative - integers, we take $x=-14$. Then the other integer is $x + 5=-14 + 5=-9$.

Step5: Calculate the sum

The sum of the two integers is $-14+( - 9)=-23$.

Answer:

-23