Answer:
x = 1.92888 (5 d.p.)
Explanation:
Given equation:

Square both sides:

Simplify:



Solve using the Newton-Rhapson method.

If f(x) = 0 then:

Differentiate f(x) to find f'(x):

This means the iteration formula is:

Let x₀ = 2.
Substitute this into the formula to find x₁:

Substitute x₁ into the iteration formula to find x₂:

Repeat until the solution is found:



Therefore, the solution to the given equation is x = 1.92888 (5 d.p.).