$$113152\cdot(1-x^{9+1})-113152\cdot(1-x) = (1-x)\cdot1088122$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = 1.01322 & x_3 = 0.8826+0.88723i \\[1 em] x_4 = 0.8826-0.88723i & x_5 = -0.72918+1.14455i & x_6 = -0.72918-1.14455i \\[1 em] x_7 = -1.29734+0.45067i & x_8 = -1.29734-0.45067i & x_9 = 0.13731+1.31364i \\[1 em] x_10 = 0.13731-1.31364i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 113152\cdot(1-x^{9+1})-113152\cdot(1-x) &= (1-x)\cdot1088122&& \text{simplify left and right hand side} \\[1 em]113152\cdot(1-x^{10})-113152\cdot(1-x) &= 1088122-1088122x&& \\[1 em]113152-113152x^{10}-(113152-113152x) &= -1088122x+1088122&& \\[1 em]113152-113152x^{10}-113152+113152x &= -1088122x+1088122&& \\[1 em]113152-113152x^{10}-113152+113152x &= -1088122x+1088122&& \\[1 em]-113152x^{10}+113152x &= -1088122x+1088122&& \text{move all terms to the left hand side } \\[1 em]-113152x^{10}+113152x+1088122x-1088122 &= 0&& \text{simplify left side} \\[1 em]-113152x^{10}+1201274x-1088122 &= 0&& \\[1 em] \end{aligned} $$
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