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^21-(-15)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (0 -  22x21) -  -15  = 0 

Step  2  :

Trying to factor as a Difference of Cubes:

 2.1      Factoring:  15-4x²¹ 

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 :  15  is not a cube !!

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

Equation at the end of step  2  :

  15 - 4x21  = 0 

Step  3  :

Solving a Single Variable Equation :

 3.1      Solve  :    -4x²¹+15 = 0 

 Subtract  15  from both sides of the equation : 
                      -4x²¹ = -15
Multiply both sides of the equation by (-1) :  4x²¹ = 15


Divide both sides of the equation by 4:
                     x²¹ = 15/4 = 3.750
                     x  =  21st root of (15/4) 

 The equation has one real solution
This solution is  x = 21st root of ( 3.750) = 1.06496

One solution was found :