SOLUTION: why can't we solve each and every problem by quadratic formula???why we need to use factorizing method or completing square method????we have formula then why we need to study comp

Question 664883: why can't we solve each and every problem by quadratic formula???why we need to use factorizing method or completing square method????we have formula then why we need to study completing square method????
Found 2 solutions by mananth, vleith:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Just think of it as another tool in your mathematics toolbox.

Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
It's a fair question, especially if you are new to algebra.
Why do you need to know how to factor? Many times the 'answer' is not a number, but an algebraic term. Many times you can get to that more easily by factoring. Plus you will be asked to solve by factoring on SATs, so better get ready.
As far as completing the square goes, if you saw a proof of the quadratic equation, you saw an real instance where completing the square matters. If you have not seen a proof of the quadratic equation, try solving it yourself or doing a web search to find (and understand) a proof. Knowing the method is a good thing to know. Plus, again, many times the 'answer' is not going to end up being a number (real or imaginary). It will end up being algebraic. Getting that may be easier using squares method.
The squares method is also helpful (for me anyway) when the order of the given problem is some even power greater than 2 (4, 6, 8 etc). Some problems can be more easily attacked using complete the square when the square being used contains power of a variable higher than 2. This will happen down the road. So for now, accept my assertion that in many cases 'the method IS the answer'. Think of it thiy. If you are a carpenter, the more tools you have and know how to use, the more equipped you will be when facing a wide set of problems.
Same for mathematics. Learn all the tools. Use the one most suited to the given task (which often IS the quadratic equation). But be aware that as you move into higher forms of mathematics, it is the methods and processes (the way one thinks and abstracts) that port to the more advanced levels.
Math (and much of our physical world) is pattern based. The more patterns you 'see' and the more processes you have to address those patterns, the better off you are.

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