While I understand what you are doing it is the first time I see this approach pretending to be a well defined method.
So I know I need to use "X is small method" before I move on to the "method of successive approximations."
.355 = 4x2 / (2.83)2(2.83) Did I do something wrong at this step?
solving for x.. x =1.42
Now I check the ratio to make sure its less than 5% deviation
1.42/2.83 = 50% ..WAY off. Did I do something wrong at this step?
Assuming your math is OK you know "x is small" approximation is wrong in this case.
So now I am supposed to use this ridiculous method of successive approximation.
Nothing ridiculous about iterative methods - actually their variants are basis of many numerical methods.
So I plug the value of x (from the smaller amount method) back into the equation and solve until I get a number close the value of x.
No idea why you want to start with the x values calculated earlier - not that it is a bad starting point, I just fail to see why it is better than any other.
.355 = 4x2 / (2.83-2(1.42))2(2.83-(1.42)
You better rearrange your equation to the form xn+1
), then it is easy to either write a program or even use a spreadsheet for calculations.