9x^2 = 64

Date: 03/22/2003 at 16:54:38
From: Tanya
Subject: Zero-Factor Theorem

I am trying to figure out what 9x^2 = 64 is.  

I am not sure how this relates to the zero factor theorem.  Am I 
looking to make the answer 0?

Date: 03/22/2003 at 21:55:26
From: Doctor Ian
Subject: Re: Zero-Factor Theorem

Hi Tanya, 

If x were zero, then it would be the case that

  9(0^2) = 64

       0 = 64

and that's not the case. 

Let's look at a similar question:

  25x^2 = 49

Now, I can divide both sides of an equation by the same thing, so long
as the thing isn't zero (because we can't divide by zero). So I'll 
divide both sides by 25:

  25x^2   49
  ----- = --
   25     25

          49
    x^2 = --
          25
             ___
            | 49
      x =   | --
           \| 25

Now, what's interesting is that 49 and 25 are both perfect squares:

             ______
            | 7 * 7
      x =   | -----
           \| 5 * 5

             __      __
            | 7     | 7
      x =   | -  *  | -
           \| 5    \| 5

             
           7 
      x =  - 
           5 

Kind of interesting how it works out, isn't it? 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/