## x(x+5)=0, can't divide by zero question

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
mickwid
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Joined: Wed Nov 30, 2011 1:31 am
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### x(x+5)=0, can't divide by zero question

Hello,

I'm from Hong Kong and I have a question related to your page http://www.purplemath.com/modules/solvquad.htm. x(x+5)=0. You mentioned that "But you can't divide by zero". I would like to clarify if you mean "divide by zero" is conceptually wrong, or divide by zero in this equation can only lead to answer of x=1 and can't lead to x=0 so it is not a good idea.

Another very simple one: x(x+1)=2x, find x. Similarly, x=0 or x=1 like this:

x(x+1)=2x
x^2+x-2x=0
x^2-x=0
x(x-1)=0 <== same as your x(x+5)=0

If we solve like this:

x(x+1)=2x
x(x+1)/=2x/x
x+1=2
x=1

We know that we can never find the answer of x=0 in this way, but is this way "wrong" or "not good"?

Also, if something like xy=3x^2, can we "dividing off the x" to achieve y=3x?
xy/x=3x^2/x
y=3x

This is similar that x can be zero or not and "But you can't divide by zero" apply here or not?

Thank you,
Mickwid.

little_dragon
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Joined: Mon Dec 08, 2008 5:18 pm
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### Re: x(x+5)=0, can't divide by zero question

I would like to clarify if you mean "divide by zero" is conceptually wrong, or divide by zero in this equation can only lead to answer of x=1 and can't lead to x=0 so it is not a good idea.
it means U cant do it!
"div by zoer" doesnt mean anything!
its against the rules of math!

nona.m.nona
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Joined: Sun Dec 14, 2008 11:07 pm
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### Re: x(x+5)=0, can't divide by zero question

Division by zero is "undefined", meaning that the process has no defined value or definition. The process of dividing by zero is disallowed.