Question about settings equations equal to eachother

[939]

Homework Statement

Just wondering if there is a set rule here. What I'm not sure about is which side moves to the other.

Homework Equations

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

The Attempt at a Solution

x^2 = 8 - x^2
or
8 - x^2 = x^2

Option 1: Move left to right
= 8 - 2x^2

Option 2: Move right to left
= 2x^2 - 8

Which method are you supposed to use?

When finding zeroes you'll get the same answer either way, but sometimes (i.e. integrating) it seems like you'll get different answers depending on which way you went...

 

[Mark44]

Homework Statement

Just wondering if there is a set rule here. What I'm not sure about is which side moves to the other.

It doesn't matter, as long as what you're doing is mathematically valid.

Homework Equations

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

The Attempt at a Solution

x^2 = 8 - x^2
or
8 - x^2 = x^2

Option 1: Move left to right
= 8 - 2x^2

Option 2: Move right to left
= 2x^2 - 8

Both of these are wrong, because you have lost one side of the equation.
In option 1, the equation is really 0 = 8 - 2x²
In option 2, the equation is really 0 = 2x² - 8

Both equations have exactly the same solution set.

Which method are you supposed to use?

When finding zeroes you'll get the same answer either way, but sometimes (i.e. integrating) it seems like you'll get different answers depending on which way you went...

Can you give an example of a situation where you're getting different answers?

 

[939]

It doesn't matter, as long as what you're doing is mathematically valid.
Both of these are wrong, because you have lost one side of the equation.
In option 1, the equation is really 0 = 8 - 2x²
In option 2, the equation is really 0 = 2x² - 8

Both equations have exactly the same solution set.

Can you give an example of a situation where you're getting different answers?

Thanks, there are no such examples, it was just me making errors. I appreciate it.