To solve the equation $\cos(x) + 0.3x = 0$ using numerical methods, we can use iterative techniques such as the Newton-Raphson method or Bisection method to find the positive root.

1. Newton-Raphson Method

The Newton-Raphson method requires the function and its derivative. The equation can be rewritten as:

$f(x) = \cos(x) + 0.3x = 0$

To apply the method, we first need the derivative $f'(x)$:

$f'(x) = -\sin(x) + 0.3$

The Newton-Raphson formula is:

$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$

where $f(x)$ is the original function and $f'(x)$ is its derivative.

Now we can apply this method with an initial guess, say $x_0 = 1$, and iterate until the solution converges.

2. Bisection Method

Alternatively, we can use the Bisection Method, which is simpler but requires us to find an interval $[a, b]$ where $f(a)$ and $f(b)$ have opposite signs. We can check values of $f(x)$ at various points to locate such an interval and then repeatedly halve the interval until the solution converges.

Would you like me to apply the Newton-Raphson method and calculate the solution for you numerically?