1. ## equation 1

$\displaystyle \begin{array}{l} solve\;in\;R \\ \\ x^4 - 2x^2 - 400x = 9999 \\ \end{array}$

2. Bring everything to one side

$\displaystyle x^4 - 2x^2 - 400x - 9999 = 0$.

Now work out the factors (positive and negative) of $\displaystyle 9999$.

Substitute each of these factors into the polynomial.

By the factor theorem, if any of these factors (call it $\displaystyle a$) makes the polynomial $\displaystyle = 0$, then $\displaystyle x - a$ is a factor.

3. Solve in R? Do you mean for the real solutions?

Anyway, rearrange;

$\displaystyle x^4 - 2x^2 - 400x - 9999= 0$

Then, I'll use the factor theorem.

Let f(x) = x^4 - 2x^2 - 400x - 9999

By trial and error, find the values of x that are factors of 9999 that make f(x) = 0. Those are the factors of your equation.

Use long division or inspection to divide f(x) by their factors to get other factors, until you get a quadratic which is more easily factorised.

If it cannot be solved, then the values you got for f(x) = 0 are the only solutions.

EDIT: Woops, too late... I was making sure there were solutions =S