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The equation $100\sqrt{x_1} = 8x_1^{3/2} - 5$ is cubic in $\sqrt{x_1}$. Unless you have been asked for an analytic solution (which is possible but complex), the approximate method I suggest is first to ignore the minus $5$, enabling division by $\sqrt{x_1}$ yielding: $$100 = 8x_1$$ The first approximation is then $x_1 = 100/8 = 12.5$. Since $100\sqrt{12.5} \...


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