Answer:

Explanation:
Let's call the two consecutive negative integers x and x - 1.
We know that the sum of their squares is equal to 113, so we have the equation:

Expanding the squares on the left-hand side, we get:

Combining like terms, we get:

Subtracting 1 and 2x from both sides, we get:

Dividing both sides by 2, we get:


Factoring the left-hand side, we get:


x(x-8) +7(x-8)=0
(x-8)(x+7)=0
Setting each factor equal to 0, we get:

Solving for x we get:

Since x is negative, the only solution that works is x = -7.
Here 8 is positive while squaring we get 64 for (-8) too.
So, another negative integer is -8.
Therefore, the two consecutive negative integers that add up to 113 are -7 and -8. The sum of their squares is:
