Rearranging simple equation by making x the subject: 205 = ((4*pi*x*f)/c)^2

[duckau]

Hi,

It's been a while and I'm a bit rusty.. I am attempting to rearrange the following equation to make x the subject:

205 = ((4*pi*x*f)/c)^2I have attempted:

205/x^2 = ((4*pi)^2*f^2) / c^2
x^2/205 = c^2/(4*pi)^2*f^2

then

x^2 = 205 * (c^2/((4*pi)^3)*f^2)
x = \sqrt{205*(c^2/((4*pi)^2)*f^2)}

Unfortunately my answer doesn't evaluate. Any tips on my process?

Thanks!

 

[Greg]

Hi duckau and welcome to MHB! :D

$$205=\left(\frac{4\pi x f}{c}\right)^2$$

$$\pm\sqrt{205}=\frac{4\pi x f}{c}$$

$$\pm\frac{\sqrt{205}c}{4\pi f}=x$$

Does that help?

 

[HallsofIvy]

"Back out" of the expression by "undoing" each thing that was done to x:
We have $\left(\frac{4\pi x f}{c}\right)^2= 205$. Since the last thing done is squaring, the first thing we do is take the square root of each side: $\frac{4\pi x f}{c}= \pm\sqrt{205}$. On the left we are dividing by c so multiply both sides by c: $4\pi x f= \pm c\sqrt{205}$. We now have x multiplied by $4\pi f$ so, finally, divide both sides by $4\pi f$:

$x= \pm \frac{c\sqrt{205}}{4\pi f}$.

 

[duckau]

Thanks a lot.. that's exactly what I was after.

I appreciate the advice regarding working backwards instead of attempting to solve the equation!

Regards.