so i divide both side by x
but this is incorrect. why?
If you divide both sides by 1, you "miss" the solution x=0.
the two solutions are :
- x such that x=0
- x such that 2x+11=0
Remember that you can divide by x only if x different from zero!
So in case you choose to divide by x, you must precise that x is different from zero.
And then to be thorough you need to examine what happens when x takes the value 0.
This is why it is safer not to divide but factorise.
Quadratic equations sometimes have a common factor containing the unknown quantity. In such cases, dividing by the common factor leads to the loss of a solution.
(dividing by )
The solution has been lost.
Although dividing an equation by a NUMERICAL common factor is correct and sensible, dividing by a common factor containing the unknown quantity results in the loss of a solution.
Bring everything to one side, and put
Either or .
I hope that helps.