An Algorithmic solution is a solution that involves a series of actions/steps. For example, baking a cake.
A Heuristic solution is a solution that requires knowledge, experience, and sometimes trial and error. For example, buying the best stock.
While some problems require only one type of solution, most problems require a combination of the two different types of solutions.
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There is no difference between real solutions and real roots.
The word heuristic is derived form the Greek word "heuriskein", which is related to the concept of finding something. Metaheuristics on the other hand is simply the combination of the word heuristics with the prefix meta, which means advance level of heuristic.
There is only one solution: x = 15. Consequently the remainder of the question is nonsense.
difference between as on and as at
Solutions may be closed or open regions or they may be points within a region (for example, grid points for integer solutions), or points of intersection between curves or between curves and the axes. It all depends on what the graphs and the solutions are.