To solve for c, we can use the fact that x1 - x2 = 6.

We know that the roots of a quadratic equation in the form ax^2 + bx + c = 0 are given by the formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, our equation is x^2 + x + c = 0. Comparing with the quadratic equation formula, we can see that a = 1, b = 1, and c = c.

The roots are given by:

x1 = (-1 + √(1 - 4c)) / 2

x2 = (-1 - √(1 - 4c)) / 2

Given that x1 - x2 = 6:

(-1 + √(1 - 4c)) / 2 - (-1 - √(1 - 4c)) / 2 = 6

Simplifying this expression, we get:

√(1 - 4c) = 7

Squaring both sides to eliminate the square root:

1 - 4c = 49

4c = -48

c = -12

Therefore, the value of c is -12.