Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "k1"   was replaced by   "k^1". 

Rearrange:

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

                     k^10-(27)=0 

Step by step solution :

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  k¹⁰-27 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 27 is not a square !!

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

Equation at the end of step  1  :

  k10 - 27  = 0 

Step  2  :

Solving a Single Variable Equation :

 2.1      Solve  :    k¹⁰-27 = 0 

 Add  27  to both sides of the equation : 
                      k¹⁰ = 27
                     k  =  10th root of (27) 

 The equation has two real solutions  
 These solutions are  k = ± 10th root of 27 = ± 1.3904  
 

Two solutions were found :