Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "p1"   was replaced by   "p^1". 

Rearrange:

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

                     3*p^10-(16)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  3p10 -  16  = 0 

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  3p¹⁰-16 

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 :  3  is not a square !!

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

Equation at the end of step  2  :

  3p10 - 16  = 0 

Step  3  :

Solving a Single Variable Equation :

 3.1      Solve  :    3p¹⁰-16 = 0 

 Add  16  to both sides of the equation : 
                      3p¹⁰ = 16
Divide both sides of the equation by 3:
                     p¹⁰ = 16/3 = 5.333
                     p  =  10th root of (16/3) 

 The equation has two real solutions  
 These solutions are  p = 10th root of ( 5.333) = ± 1.18222  
 

Two solutions were found :