How would I solve this equation?

Question

x(1+x)^50 / (1+x)^50-1 * 20000 = 476.75

Answer 1

We are given the equation:

\[

\frac{x(1 + x)^{50}}{(1 + x)^{50} - 1} \times 20000 = 476.75

\]

### Step 1: Simplify the equation

Divide both sides by 20000 to isolate the fraction:

\[

\frac{x(1 + x)^{50}}{(1 + x)^{50} - 1} = \frac{476.75}{20000}

\]

Simplifying the right-hand side:

\[

\frac{476.75}{20000} = 0.0238375

\]

Now the equation becomes:

\[

\frac{x(1 + x)^{50}}{(1 + x)^{50} - 1} = 0.0238375

\]

### Step 2: Solve for \(x\)

At this point, solving for \(x\) requires iterative or numerical methods, as the equation involves exponents. The next step is to use a numerical solver like Newton's method or software to approximate \(x\).

Answer 2

Can't say how you would solve, yet here is mine:

x(1 + x) = 0.0238375, Law of Exponents, Division Property of Equality

x + x² = 0.0238375

Leave it to you to solve a quadratic.