# Thread: I'm so stuck yet probably so easy, what am I missing?...

1. ## I'm so stuck yet probably so easy, what am I missing?...

Hi. I have been trying to solve this for weeks add can't figure it out.

I need to solve for 'b' in this equation:
(ie, I need to be able to reverse the equation so if given 'z' then I can find b. 'a' is just a constant).

$\displaystyle z = ab / sqrt (a^2 - b^2)$

Please if anyone can save me and show me how to do this. Thank you so much in advance.

(not sure if this image will show):

2. Originally Posted by lenfromkits
Hi. I have been trying to solve this for weeks add can't figure it out.

I need to solve for 'b' in this equation:
(ie, I need to be able to reverse the equation so if given 'z' then I can find b. 'a' is just a constant).

$\displaystyle z = ab / sqrt (a^2 - b^2)$

Please if anyone can save me and show me how to do this. Thank you so much in advance.

(not sure if this image will show):
Square both sides:
$\displaystyle z = \frac{ab}{\sqrt{a^2 - b^2}} \implies z^2(a^2 - b^2) = (ab)^2$

Group terms with $\displaystyle b^2$:

$\displaystyle z^2(a^2 - b^2) = (ab)^2 \implies z^2a^2 = (z^2+a^2)b^2$

Finally,
$\displaystyle z^2a^2 = (z^2+a^2)b^2 \implies b^2 = \frac{a^2z^2}{a^2 + z^2}$

3. ## see, just like I said, easy....

...for a pro. Thank you so much! I get it now. I couldn't see the way but you make it seem easy.