The equation (0.01)^x + 9.9*(0.1)^x - 1 = 0 is a nonlinear equation in terms of x.

Let's substitute (0.1)^x = y for easier manipulation:

(0.01)^x + 9.9y - 1 = 0
y^2 + 9.9y - 1 = 0

Now we have a quadratic equation in terms of y:

y = [-9.9 ± √(9.9^2 + 4)] / 2
y = [-9.9 ± √(98.01)] / 2
y = [-9.9 ± 9.9] / 2

Therefore, y = -9.9 + 9.9 / 2 or y = -9.9 - 9.9 / 2

Solving for y, we get:
y = 0 or y = -9.9

Substitute back:
(0.1)^x = 0 or (0.1)^x = -9.9

Since (0.1)^x can never be negative or equal to -9.9, the equation has no real solutions.