Solution: Given the supply equation p=0.2 q^3+0.5 q+2 and the demand equation p=10-q, use Newton's method to estimate the market equilibrium quantity,

Question: Given the supply equation

\[p=0.2 q^{3}+0.5 q+2\]

and the demand equation $p=10-q$, use Newton's method to estimate the market equilibrium quantity, and find the corresponding equilibrium price. Use 5 as an initial estimate for the required value of $q$, and give your answer to two-decimal-place accuracy.

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Solution: Given the supply equation p=0.2 q^3+0.5 q+2 and the demand equation p=10-q, use Newton's method to estimate the market equilibrium quantity,

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