-88s18-64s17+24s13=8s13()
To solve the equation \(-88s^{18} - 64s^{17} + 24s^{13} = 8s^{13}()\), we first rearrange it to isolate the terms on one side.
Starting from:
\[ -88s^{18} - 64s^{17} + 24s^{13} - 8s^{13} = 0 \]
This simplifies to:
\[ -88s^{18} - 64s^{17} + (24 - 8)s^{13} = 0 \]
This can be written as:
\[ -88s^{18} - 64s^{17} + 16s^{13} = 0 \]
Now, we can factor out a common term. Notice that \(s^{13}\) is a common factor for the \(16s^{13}\) term:
\[ s^{13}(-88s^{5} - 64s^{4} + 16) = 0 \]
This equation can be satisfied if either \(s^{13} = 0\) or the polynomial factor \( -88s^{5} - 64s^{4} + 16 = 0\).
From \(s^{13} = 0\), we get \(s = 0\).
To solve the polynomial part \( -88s^{5} - 64s^{4} + 16 = 0\), we can rewrite it as:
\[ 88s^{5} + 64s^{4} - 16 = 0 \]
This polynomial may not have simple roots, and numerical methods or specific solvers may apply to find roots if necessary.
Thus, the solutions to the original equation are:
- \(s = 0\)
- Additional solutions from the polynomial \(88s^{5} + 64s^{4} - 16 = 0\).
If you need numerical solutions for the polynomial, please clarify and I can assist further.
