Solving for x with A, b, and c Given

• Toby_Obie
In summary, This conversation is about trying to rearrange an equation to solve for the variable x. The equation involves the values A, b, and c, and has a complicated denominator. The participants discuss different methods and the possibility of finding a general solution, but ultimately it is concluded that for most values of c, the equation cannot be solved exactly. One participant suggests using Excel's Goal Seek function as a helpful tool.
Toby_Obie
Hello,

Im trying to rearrange to find x from the below (all other values, A, b and c known)

$$A = bx / 1-(1+x)^-c$$

I've rearranged but to no avail, I'm unsure how to isolate x

Any input much appreciated

Thanks

Hello Toby!

(you needed to put the index in curly brackets, {-c}, since it had more than one character … alternatively, try using the X2 tag just above the Reply box )

This is the same as (1 + x)-c = 1 - (b/A)x …

I don't think there is a "simple" solution.

But why are you looking for one?

Noted

I've never come up against an equation like this before, just curious whether it can be solved for x ? (new skills)

Is there a general solution to this type of equation ?

Can you point me in the right direction ?

Thanks very much

Toby_Obie said:
Is there a general solution to this type of equation ?

I don't think so.

Real life just isn't that convenient!

Thanks anyway

Anybody else think they know the answer ?

Really, the problem is very complicated to solve, and for most $c\geq 4$ it's likely impossible to solve!

There is a proof that says for polynomials of degree 5 or higher, there is no way to solve the equation in its general case like quartics and below have been.

Okay

I'm using Excel to approximate x for known values of A, b, c

Thanks anyways

Just a note

Excel Goal Seek function solved my function to 4 decimal places, good tool

1) What is the formula for solving for x with A, b, and c given?

The formula for solving for x with A, b, and c given is x = (-b ± √(b^2 - 4ac)) / 2a.

2) Can you explain the variables A, b, and c in the formula?

A, b, and c are coefficients in a quadratic equation, where A represents the coefficient of the squared term, b represents the coefficient of the linear term, and c represents the constant term.

3) How do I know which value to use for the plus or minus sign in the formula?

The plus or minus sign in the formula is used to account for both possible solutions of a quadratic equation. You can use both values to determine which solution is the correct one based on the given context of the problem.

4) What if the value inside the square root is negative?

If the value inside the square root is negative, the equation does not have any real solutions. This can happen when the discriminant (b^2 - 4ac) is negative, indicating that the quadratic equation does not intersect with the x-axis.

5) Are there any other methods for solving for x with A, b, and c given?

Yes, there are other methods such as factoring or using the quadratic formula. However, the formula for solving for x with A, b, and c given is the most straightforward and reliable method for finding the solutions to a quadratic equation.

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