How to get from this equation x^3 + 4x^2-10=0 to this equation x = x - [(x^3 + 4x^2-10)/ (3x^2+8x)]

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How to get from this equation x^3 + 4x^2-10=0 to this equation x = x - [(x^3 + 4x^2-10)/ (3x^2+8x)]

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so the original equation we divide it by -(3x^2+8x) assuming that this in not zero because you cannot divide by zero so we have (x^3+4x^2-10)/[-(3x^2+8x]=0 -(x^3+4x^2-10)/(3x^2+8x)=0 now add x no both sides x-(x^3+4x^2-10)/(3x^2+8x)=x
on not no
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not really, thanks thou for help. I am still thinking about our solution
you wanted to know how to write that one equation as that other equation right? you didn't want to use newton's method to find the x-intercepts? did you?
f(x) = x^3 + 4x^2 -10 = 0 x^3 + 4x^2 -10 = 0 x^3 + 4x^2 = 10 x^2 = 10/(4+x) x = g4(x) = (10/(4+x))^(1/2) f(x) = x^3 + 4x^2 -10 = 0 x^3 + 4x^2 -10 = 0 4x^2 = x^3 + 10 x^2 = (-x^3 + 10)/4 x = ((-x^3 + 10)/4)^0.5 x = g3(x) = ((-x^3 + 10)/4)^0.5 f(x) = x^3 + 4x^2 -10 = 0 x^3 + 4x^2 -10 = 0 x^3 = 10 - 4x^2 x^2 = (10 - 4x^2)/x x = g2(x) = ((10 - 4x^2)/x)^(1/2) see all these equations I didn't need to add or divide any extra equations. However, your answer looks good, but you did add extra stuff there to reach the second equation. I am wondering if there will be anyway to reach the second equation without adding extra things in the original equation
I am trying here to solve the original equation for x. There are five ways to solve the equation for x, I only got four ways.
are you in calculus?
numerical analysis
so you do know newton's method?
yes I do
that second equation is looks like newton's method x1=x0-f(x0)/f'(x0) f'(x0) not equal to zero
I know about the newton's method. I need to solve the original equation for x in five different ways, then I need to verify that each of the five equations converges with the same fixed point of original equation. I know three of them will converge, except one. I got to figure out how to find the fifth equation
I know about the newton's method. I need to solve the original equation for x in five different ways, then I need to verify that each of the five equations converges with the same fixed point of original equation. I know three of them will converge, except one. I got to figure out how to find the fifth equation

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