Newton's method?

Question

Use Newton's method to find all the roots of the equation e^-x = 7+x correct to eight decimal places.

Answer 1

e^-x = 7 + x
y = 7 + x - e^-x = 0
∆y/∆x = 1 + e^-x
∆y/(1 + e^-x) = ∆x
x = x + (e^-x - x - 7)/(1 + e^-x)
0
-3
-2.237129366
-1.79304731
-1.678776483
-1.672836611
-1.672821699
-1.672821699