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 :

                     4*x^212*x-(135)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (22x212 • x) -  135  = 0 
 Step  2  :

Trying to factor as a Difference of Cubes:

 2.1      Factoring:  4x²¹³-135 

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 :  4  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Equation at the end of step  2  :

  4x213 - 135  = 0 

Step  3  :

Solving a Single Variable Equation :

 3.1      Solve  :    4x²¹³-135 = 0 

 Add  135  to both sides of the equation : 
                      4x²¹³ = 135
Divide both sides of the equation by 4:
                     x²¹³ = 135/4 = 33.750
                     x  =  213th root of (135/4) 

 The equation has one real solution
This solution is  x = 213th root of (33.750) = 1.01666

One solution was found :