Solution - Nonlinear equations

Step by step solution :

Step  1  :

Trying to factor as a Difference of Cubes:

 1.1      Factoring:  x²⁷-16 

Theory : A difference of two perfect cubes,  a³ - b³ can be factored into
              (a-b) • (a² +ab +b²)

Proof :  (a-b)•(a²+ab+b²) =
            a³+a²b+ab²-ba²-b²a-b³ =
            a³+(a²b-ba²)+(ab²-b²a)-b³ =
            a³+0+0-b³ =
            a³-b³

Check :  16  is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes

Equation at the end of step  1  :

  x27 - 16  = 0 

Step  2  :

Solving a Single Variable Equation :

 2.1      Solve  :    x²⁷-16 = 0 

 Add  16  to both sides of the equation : 
                      x²⁷ = 16
                     x  =  27th root of (16) 

 The equation has one real solution
This solution is  x = 27th root of 16 = 1.1081

One solution was found :