Solving the equation ((1+x)^(36)−1)/x=20142.9/420 for x.

Nathanial Levine

Nathanial Levine

Answered question

2022-09-30

Solving the equation ( 1 + x ) 36 1 x = 20142.9 / 420

Answer & Explanation

recreerefr

recreerefr

Beginner2022-10-01Added 7 answers

This is a standard example of an equation that does not have an explicit formula for its root. It can only be solved numerically.
The important thing is to get a good first approximation to the root.
For example, if you want to solve ( 1 + x ) n 1 x = a, and you think that there might be a root close to 0, you can approximate ( 1 + x ) n by 1 + n x + n ( n 1 ) x 2 / 2 (the first terms of the binomial theorem) to get n + n ( n 1 ) x / 2 = a
Then apply Newton's iteration.

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