Question

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)]

Answer 1

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

Answer 2

on not no

Answer 3

are there any questions?

Answer 4

not really, thanks thou for help. I am still thinking about our solution

Answer 5

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?

Answer 6

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

Answer 7

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.

Answer 8

are you in calculus?

Answer 9

numerical analysis

Answer 10

so you do know newton's method?

Answer 11

yes I do

Answer 12

that second equation is looks like newton's method
x1=x0-f(x0)/f'(x0)
f'(x0) not equal to zero

Answer 13

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

Answer 14

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