# Thread: Moving variable to other side of equation

1. ## Moving variable to other side of equation

I'm having trouble moving terms from one side of an equation to another, particularly when I'm trying to make an equation equal to 0.

For example:

8= x^1-2x

Can someone explain o me why

-x^2+2x+8=0 is WRONG and why 0=x^2-2x-8 is RIGHT?

Thanks

2. Originally Posted by schoolboydj
I'm having trouble moving terms from one side of an equation to another, particularly when I'm trying to make an equation equal to 0.
Originally Posted by schoolboydj

For example:

8= x^1-2x I will assume that x^1 is supposed to be x^2.

Can someone explain o me why

-x^2+2x+8=0 is WRONG and why 0=x^2-2x-8 is RIGHT?

Thanks
Hi DJ:

Who told you that moving all the terms to the left side is wrong?

Both of your results are valid; they are equivalent equations.

Cheers,

~ Mark

3. Originally Posted by schoolboydj
I'm having trouble moving terms from one side of an equation to another, particularly when I'm trying to make an equation equal to 0.

For example:

8= x^1-2x

Can someone explain o me why

-x^2+2x+8=0 is WRONG and why 0=x^2-2x-8 is RIGHT?

Thanks
Hello

When you rearrange an equation if you follow the 'rules' then the equality will remain true.

I assume you are rearranging quadratic equations to find the roots. Equating them with zero and then factoring to find the values of x that make the expression equal to zero. On a graph theses values are the x - intercepts.

I think when finding the roots of a quadratic equation it is usual to keep the
$x^2$ term positive, factoring seems easier that way.

Both of your equations are correct rearrangements of the origianl equation. They are the same, both being equal to zero. Although they have the same roots, x - intercepts, the two quadratic expressions are different.

$-x^2+2x+8 = -(x^2-2x-8)$

$y = -(x^2-2x-8)$

Is a reflection of the graph,

$y= x^2 -2x -8$

In the x axis.

See the attached graph. Thought this might help, but perhaps not. Please see Mark's post below for clarification.

4. Originally Posted by Ting
... Both of your rearranged equations are correct, but ... they are different equations.
Hi Ting:

I'm not sure of your intended meaning when you typed the adjective "different", so I would like to clarify.

There is a difference between the terms "equation" and "function".

There is no symbol y in the original post.

Both of the equations in the original post are mathematically equivalent.

If we replace the zeros with the symbol y, then we are expressing a functional relationship.

If we further state that y is the dependent variable in this functional relationship, then we can write:

y = f(x).

After these assumptions, you are correct in pointing out that the graph of f(x) is a reflection of the graph of -f(x).

Again, there is nothing wrong with either of the equations in the original post, and I'm still curious to know why the original poster thinks that there is.

Cheers,

~ Mark

5. Hello mark.

The two equation are not different, both being equal to 0, but the two quadratic expressions are different.

My post is misleading, incorrect use of terminolgy, and I will edit it accordingly.

Best wishes

Ting