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When you analyze a problem you look it over which is what analyzing means. You look over the problem and then you solve it. When you solve a problem you solve it and you use certain steps and solve it but of course everyone has there ways to solve a problem but some people have ways to solve it by just analysing it. That is the difference.
There are many different problems and different ways for solving them.
You always have the choice of doing it by calculator or by pencil.
facctor the problem and atke the square root of both sides
One has the choice of solving it by pencil or calculator.