quadratic equation or not

[BrownieDDD]

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i got this question and I don't know when or not to use the quadratic or if i am allowed to factor..

Factor method: 4a/5=a^2 ---> 4a=5a^2 --> 4=5a --->a = 4/5

Quadratic method : kaplan did this: 5a^2 - 4a=0 ---> a (5a-4)= 0 a = 0, 4/5

I have come across problems where factoring doens't lead to the correct answer. In this case, my factoring method led me to the correct answer as the quadratic method. Can anyone tell me when you must use the quadratic method and when you can factor?

 

[NewBee12]

What Kaplan did was factoring. Quadratic equation has the following format: ax^2 + bx + c. You should always factor. In your case by canceling a you cancelled an answer.
Factor then check to make sure which of the answers work.

 

[ushaseos]

Alternatively, anytime you cancel a variable try to see when it wouldn't be allowed. In your case when you divide both sides by a, you are implying it cannot equal 0 (if it does you divided both sides by 0). Once you have this restriction, check to see if it is a solution.

Of course factoring/Quadratic is always best since it is unambiguous and not tricky, but if you are very used to just cancelling common factors, it might help to look at the technicality described above.

 

[BrownieDDD]

thanks guys/girls