The equation x^2 + 1 = 0 is a quadratic equation, which means it involves a variable raised to the second power. To solve for x, we can rearrange the equation to x^2 = -1. This indicates that x must be a number whose square is negative, which is not possible within the set of real numbers. To find solutions, we turn to the set of complex numbers, where i represents the imaginary unit, defined as \sqrt-1. Thus, the solutions to the equation are x = i and x = -i, where both are examples of complex numbers.