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Use Newton's method with initial approximation x1 = −1 to find x2  the second approximation to the root of the equation x^3 + x + 7 = 0. x2 = ?

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Use the Newton iteration formula:

`x_2=x_1-f(x_1)/f'(x_1)`

 

In our case, `f(x_1)=-1-1+7=5`

`f'(x)=3x^2+1`

`f'(x_1)=3(-1)^2+1=4`

`x_2=-1-(5)/4=-9/4`

Answer: `x_2=-9/4`

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