43+42−100<0
53+52−100>0
So, the root is between 4 and 5.
x2(x+1)=100
x=x+110
Let the initial approximation be x0=4.5
x1=10/4.5+1=4.26
x2=10/4.26+1=4.35
x3=10/4.35+1=4.32
x4=10/4.32+1=4.33558
x5=10/4.33558+1=4.32921
x6=10/4.32921+1=4.33180
x7=10/4.33180+1=4.33117
Since the difference between x6 and x7 are very small, so the root is 4.33117
Comments
Dear George, please use the panel for submitting a new question.
Find the negative root of the equation x^3 - 2x + 5 =0