Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "a1"   was replaced by   "a^1". 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  5a18 -  4a  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   5a¹⁸ - 4a  =   a • (5a¹⁷ - 4) 

Equation at the end of step  3  :

  a • (5a17 - 4)  = 0 

Step  4  :

Theory - Roots of a product :

 4.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

 4.2      Solve  :    a = 0 

  Solution is  a = 0

Solving a Single Variable Equation :

 4.3      Solve  :    5a¹⁷-4 = 0 

 Add  4  to both sides of the equation : 
                      5a¹⁷ = 4
Divide both sides of the equation by 5:
                     a¹⁷ = 4/5 = 0.800
                     a  =  17th root of (4/5) 

 The equation has one real solution
This solution is  a = 17th root of ( 0.800) = 0.98696

Two solutions were found :

1.  a = 17th root of ( 0.800) = 0.98696
2.  a = 0