Part 3/5:
Simplifying the Equation
The goal at this stage is to eliminate the ( pz ) terms. By organizing and combining the resulting coefficients, we aim to cancel out specific terms to streamline the equation. Upon achieving the necessary cancellations, we can determine the value of ( K ) in relation to the coefficient ( p ). It is discovered that:
[
K = -\frac{p}{3}
]
This determination allows further simplification to occur.
Replacing and Rearranging
After finding ( K ), we substitute it back into the transformed cubic expression. The terms reconfigure to eliminate much complexity:
[
-z^3 + \frac{p^3}{27} z^3 + Q = 0
]