Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x7"   was replaced by   "x^7". 

Rearrange:

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

                     3^2*x^7-(63)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (32 • x7) -  63  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   9x⁷ - 63  =   9 • (x⁷ - 7) 

Polynomial Roots Calculator :

 3.2    Find roots (zeroes) of :       F(x) = x⁷ - 7
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  1  and the Trailing Constant is  -7.

 The factor(s) are:

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,7

 Let us test ....

Polynomial Roots Calculator found no rational roots

Equation at the end of step  3  :

  9 • (x7 - 7)  = 0 

Step  4  :

Equations which are never true :

 4.1      Solve :    9   =  0

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

Solving a Single Variable Equation :

 4.2      Solve  :    x⁷-7 = 0 

 Add  7  to both sides of the equation : 
                      x⁷ = 7
                     x  =  7th root of (7) 

 The equation has one real solution
This solution is  x = 7th root of 7 = 1.3205

One solution was found :