Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two distinct negative, integer solutions. What is the sum of all of the distinct possible integers that could be under the ink stain

Step-by-step explanation:

See the comment for complete question.

Given

----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

and

Using the above roots, the equation can be represented as:

Open brackets

To compare the above equation to , we have:

Where: and

The values of and that satisfy are:

and

and

and

and

So, the possible values of a are:

When and

When and

When and

When and

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is: