The output of Reduce is different from the output of Solve: Reduce outputs a logical expression that is equivalent to the original equation, so it never omits a solution:
The Wolfram Language also allows you to get numeric solutions for equations.
For example, you can use N on the output of Solve to get a numeric approximation for the symbolic solution:
You can also get the numeric solution directly by using NSolve, which is faster than combining N and Solve:
Use NSolve to solve a more complicated polynomial equation:
You can also use NSolve to solve systems of equations numerically. Use the same syntax as you would with Solve:
If your equations involve only linear functions or polynomials, then you can use NSolve to get numerical approximations to all the solutions. However, when your equations involve more complicated functions, there is, in general, no systematic procedure for finding all solutions, even numerically. In such cases, you can use FindRoot to search for solutions.
Use FindRoot to search for numerical solutions for x, starting at 1: