Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x3"   was replaced by   "x^3". 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (2 • (x2)) -  5x3  = 0 
 Step  2  :

Equation at the end of step  2  :

  2x2 -  5x3  = 0 

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   2x² - 5x³  =   -x² • (5x - 2) 

Equation at the end of step  4  :

  -x2 • (5x - 2)  = 0 

Step  5  :

Theory - Roots of a product :

 5.1    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 :

 5.2      Solve  :    -x² = 0 

 Multiply both sides of the equation by (-1) :  x² = 0


 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      x  =  ± √ 0  

 Any root of zero is zero. This equation has one solution which is  x = 0

Solving a Single Variable Equation :

 5.3      Solve  :    5x-2 = 0 

 Add  2  to both sides of the equation : 
                      5x = 2
Divide both sides of the equation by 5:
                     x = 2/5 = 0.400

Two solutions were found :

1.  x = 2/5 = 0.400
   
2.  x = 0