Solving a cubic equation

Answer

The problem is to solve for

in the equation

We can rewrite the equation as

This is a cubic equation. We can try integer values of

to see if we can find a solution by trial and error.

.
If

So,

is a solution.

Now we can perform polynomial division to find other solutions. Since

is a solution,

is a factor of

So,

Now we need to solve the quadratic equation

.
The discriminant is

.
Since the discriminant is negative, the quadratic equation has no real solutions.

Therefore, the only real solution is

Final Answer: The final answer is

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