Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x5"   was replaced by   "x^5". 

Rearrange:

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

                     3*x^5-(1)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  3x5 -  1  = 0 

Step  2  :

Polynomial Roots Calculator :

 2.1    Find roots (zeroes) of :       F(x) = 3x⁵-1
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  3  and the Trailing Constant is  -1.

 The factor(s) are:

of the Leading Coefficient :  1,3
 of the Trailing Constant :  1

 Let us test ....

Polynomial Roots Calculator found no rational roots

Equation at the end of step  2  :

  3x5 - 1  = 0 

Step  3  :

Solving a Single Variable Equation :

 3.1      Solve  :    3x⁵-1 = 0 

 Add  1  to both sides of the equation : 
                      3x⁵ = 1
Divide both sides of the equation by 3:
                     x⁵ = 1/3 = 0.333
                     x  =  5th root of (1/3) 

 The equation has one real solution
This solution is  x = 5th root of ( 0.333) = 0.80274

One solution was found :