Solving Equations with HeavisideTheta Functions

Question

I need to solve an equation that involves the HeavisideTheta[] function, but regardless of the method I use Mathematica returns an error message. For example,

NSolve[x*HeavisideTheta[x] == 5, x]

returns the message "This system cannot be solved with methods available to NSolve". A similar message occurs with Solve[] and Reduce[]. Clearly the solution to the equation above is x=5. The full equation I need to solve can only be solved numerically. Are there any alternative functions to solve this equation?

Answer 1

NSolve[x UnitStep[x] == 5, x]
(* {{x -> 5.}} *)

Answer 2

Try

NMinimize[{1, x*HeavisideTheta[x] == 5}, x]
(*{1., {x -> 5.}}*)