SOLUTION: Hello, I would like to solve the equation below for X, but I struggle with exponent C, which makes it kind of difficult... x = a - b*x^c

Algebra ->  Linear-equations -> SOLUTION: Hello, I would like to solve the equation below for X, but I struggle with exponent C, which makes it kind of difficult... x = a - b*x^c      Log On


   

Question 1151681: Hello,
I would like to solve the equation below for X, but I struggle with exponent C, which makes it kind of difficult...
x = a - b*x^c
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Because the x occurs both as a linear term and as a term to the power c, you can't solve the general equation for x.

For the value c=1, solving the equation is simple:

x = a-bx^1
x = a-bx
x+bx = a
x(1+b) = a
x = a/(1+b)

And you could also solve the equation if c=2:

x = a-bx^2
bx^2+x-a = 0
Then use the quadratic formula....

But for other values of c, the given equation can't be solved for x.