Solution - Nonlinear equations

Step by step solution :

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  x²⁸-18 

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 : 18 is not a square !!

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

Equation at the end of step  1  :

  x28 - 18  = 0 

Step  2  :

Solving a Single Variable Equation :

 2.1      Solve  :    x²⁸-18 = 0 

 Add  18  to both sides of the equation : 
                      x²⁸ = 18
                     x  =  28th root of (18) 

 The equation has two real solutions  
 These solutions are  x = ± 28th root of 18 = ± 1.1087  
 

Two solutions were found :