\(2x^4-9x^3-11x^2+81x=63\)
\(\Rightarrow2x^4-9x^3-11x^2+81x-63=0\)
\(\Rightarrow2x^4-2x^3-7x^3+7x^2-18x^2+18x+63x-63=0\)
\(\Rightarrow2x^3\left(x-1\right)-7x^2\left(x-1\right)-18x\left(x-1\right)+63\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(2x^3-7x^2-18x+63\right)=0\)
\(\Rightarrow\left(x-1\right)\left[x^2\left(2x-7\right)-9\left(2x-7\right)\right]=0\)
\(\Rightarrow\left(x-1\right)\left(2x-7\right)\left(x^2-9\right)=0\)
\(\Rightarrow\left(x-1\right)\left(2x-7\right)\left(x-3\right)\left(x+3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\2x-7=0\\x-3=0\\x+3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{7}{2}\\x=3\\x=-3\end{matrix}\right.\)
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