# Rearranging equations to solve for different variable.

• Jul 9th 2010, 04:09 AM
gregorykrobinson
Rearranging equations to solve for different variable.
Hi,
I've been trying to re-arrange this equation to solve for R instead of A, but I can't seem to get it past being self-referential, and if I assign values to the variables, and recalculate with my re-arrangements, I get different answers, which indicates to me that I'm doing something wrong. Here's the equation:

A=R/√(R^2+X^2)

I figure the first step should be:
A*√(R^2+X^2)=R/√(R^2+X^2)*√(R^2+X^2)
simplifying to:
A*√(R^2+X^2)=R

But that is about as far as I can get. How can I get R all on one side of the equation?
• Jul 9th 2010, 04:16 AM
mr fantastic
Quote:

Originally Posted by gregorykrobinson
Hi,
I've been trying to re-arrange this equation to solve for R instead of A, but I can't seem to get it past being self-referential, and if I assign values to the variables, and recalculate with my re-arrangements, I get different answers, which indicates to me that I'm doing something wrong. Here's the equation:

A=R/√(R^2+X^2)

I figure the first step should be:
A*√(R^2+X^2)=R/√(R^2+X^2)*√(R^2+X^2)
simplifying to:
A*√(R^2+X^2)=R

But that is about as far as I can get. How can I get R all on one side of the equation?

Square both sides:

$\displaystyle A^2 = \frac{R^2}{R^2 + x^2} \Rightarrow A^2 R^2 + A^2 x^2 = R^2 \Rightarrow A^2 x^2 = R^2 (1 - A^2 )$ etc.
• Jul 9th 2010, 04:17 AM
Also sprach Zarathustra
Quote:

Originally Posted by gregorykrobinson
Hi,
I've been trying to re-arrange this equation to solve for R instead of A, but I can't seem to get it past being self-referential, and if I assign values to the variables, and recalculate with my re-arrangements, I get different answers, which indicates to me that I'm doing something wrong. Here's the equation:

A=R/√(R^2+X^2)

I figure the first step should be:
A*√(R^2+X^2)=R/√(R^2+X^2)*√(R^2+X^2)
simplifying to:
A*√(R^2+X^2)=R

But that is about as far as I can get. How can I get R all on one side of the equation?

Try to take a square both sides of the equation...

EDIT: MINUTE LATE
• Jul 9th 2010, 09:55 AM
gregorykrobinson
Ok, thanks for the help so far.

Can't believe that it didn't occur to me to square both sides.
So I understand:
$\displaystyle A=\frac{R}{\sqrt{R^2+X^2}} => A^2=\frac{R^2}{R^2+X^2}$

But then I get lost at the next step you propose:
$\displaystyle A^2=\frac{R^2}{R^2+X^2} => A^2R^2+A^2X^2=R^2$
The steps after that are a mystery to me as well:
$\displaystyle A^2R^2+A^2X^2=R^2 => A^2R^2+X^2=R^2$
$\displaystyle A^2R^2+X^2=R^2 => A^2X^2=R^2(1-A^2)$
$\displaystyle A^2X^2=R^2(1-A^2) => \frac{A^2X^2}{1-A^2}=R^2$

But you did leave me one last step to do myself, which I do comprehend:
$\displaystyle \frac{A^2X^2}{1-A^2}=R^2 => \sqrt{\frac{A^2X^2}{1-A^2}}=R$

Now I guess it shows how rusty I am, but I really would like to understand correctly.
If someone could walk me through and explain what's happened and why in each step, it would be greatly appreciated. I've got a whole HEAP of these to do, and it's going to make my life a lot easier if I can do my own homework (figure of speech, it's not really homework, just brushing up on some of my electronics theory).

I really appreciate any and all help!

EDIT:
PS. I just discovered the LaTeX features of your site, after reading through the "How NOT to get help" thread.
On becoming aware that the members here appreciate equations being submitted in this format, I went about trying to learn how to format in this way. However, I would like to make the suggestion that a tutorial be more easily found. My instinct was to look in the FAQ section, but there was no guide there. I then searched the forum itself, but most of the mention of LaTeX in threads was old, and most had dead links.
Perhaps I missed something really obvious, feel free to point out if I'm in error.
Just thought it might be worth including a Tutorial under the FAQ section.
• Jul 9th 2010, 10:29 AM
Also sprach Zarathustra
Great! Welcome to LaTex world!
• Jul 9th 2010, 06:49 PM
mr fantastic
Quote:

Originally Posted by gregorykrobinson
Ok, thanks for the help so far.

Can't believe that it didn't occur to me to square both sides.
So I understand:
$\displaystyle A=\frac{R}{\sqrt{R^2+X^2}} => A^2=\frac{R^2}{R^2+X^2}$

But then I get lost at the next step you propose:

$\displaystyle A^2=\frac{R^2}{R^2+X^2} => A^2R^2+A^2X^2=R^2$ Mr F says: To get this you multiply both sides by R^2 + x^2 and then expand.

The steps after that are a mystery to me as well:

$\displaystyle A^2R^2+A^2X^2=R^2 => A^2R^2+X^2=R^2$ Mr F says: I never wrote this.

$\displaystyle A^2R^2+X^2=R^2 => A^2X^2=R^2(1-A^2)$ Mr F says: I never wrote this either. There is an A^2 missing on the left hand side of the first equation.

I wrote $\displaystyle A^2R^2+ A^2 X^2=R^2 => A^2X^2=R^2(1-A^2)$. To get this you subtract $\displaystyle A^2 R^2$ from both sides and then factorise.

$\displaystyle A^2X^2=R^2(1-A^2) => \frac{A^2X^2}{1-A^2}=R^2$

[snip]

Since you have to solve for R, there is still at least one more step to go.