Solution - Linear equations with one unknown

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     z^212*z-(7)=0 

Step by step solution :

Step  1  :

Trying to factor as a Difference of Cubes:

 1.1      Factoring:  z²¹³-7 

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

Equation at the end of step  1  :

  z213 - 7  = 0 

Step  2  :

Solving a Single Variable Equation :

 2.1      Solve  :    z²¹³-7 = 0 

 Add  7  to both sides of the equation : 
                      z²¹³ = 7
                     z  =  213th root of (7) 

 The equation has one real solution
This solution is  z = 213th root of 7 = 1.0092

One solution was found :