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 :

                     5*x^45-(30)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  5x45 -  30  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   5x⁴⁵ - 30  =   5 • (x⁴⁵ - 6) 

Trying to factor as a Difference of Cubes:

 3.2      Factoring:  x⁴⁵ - 6 

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

Equation at the end of step  3  :

  5 • (x45 - 6)  = 0 

Step  4  :

Equations which are never true :

 4.1      Solve :    5   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

 4.2      Solve  :    x⁴⁵-6 = 0 

 Add  6  to both sides of the equation : 
                      x⁴⁵ = 6
                     x  =  45th root of (6) 

 The equation has one real solution
This solution is  x = 45th root of 6 = 1.0406

One solution was found :