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

• MHB
• duckau
In summary, the conversation discusses rearranging an equation to make x the subject. After several attempts, the solution is found by "undoing" each step that was done to x. The final solution is x = ± c√205/(4πf).
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!

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?

"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 $4\pi f$:

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

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.

## What is the equation and what does it represent?

The equation is 205 = ((4*pi*x*f)/c)^2 and it represents a mathematical relationship between the variables x, f, and c.

## Why is it necessary to rearrange the equation and make x the subject?

Rearranging the equation and making x the subject allows us to solve for the value of x, which is often the desired outcome in mathematical calculations and experiments.

## What is the process for rearranging the equation and making x the subject?

The process involves isolating x on one side of the equation by performing inverse operations on the other variables. In this case, we would divide both sides by 4*pi*f and then take the square root of both sides to solve for x.

## What are some applications of this equation?

This equation is commonly used in physics and engineering, particularly in calculations involving frequency, wavelength, and the speed of light. It can also be used to determine the unknown variable x in a variety of other scenarios.

## Are there any limitations to this equation?

As with any mathematical equation, there are limitations to its applicability. This equation is based on certain assumptions and may not accurately represent all real-world situations. Additionally, it may not be the most appropriate equation to use in all scenarios, as there may be other equations that better describe the relationship between the variables.

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