Solution - Linear equations with one unknown

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (((2 • (2x - 1) • -1) • -x) • 1) • x  = 0 

Step  2  :

Equation at the end of step  2  :

  ((-2 • (2x - 1) • -x) • 1) • x  = 0 

Step  3  :

Equation at the end of step  3  :

  (2x • (2x - 1) • 1) • x  = 0 

Step  4  :

Equation at the end of step  4  :

  2x • (2x - 1) • x  = 0 

Step  5  :

Multiplying exponential expressions :

 5.1    x¹ multiplied by x¹ = x^{(1 + 1)} = x²

Equation at the end of step  5  :

  2x2 • (2x - 1)  = 0 

Step  6  :

Theory - Roots of a product :

 6.1    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 :

 6.2      Solve  :    2x² = 0 

 Divide both sides of the equation by 2:
                     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 :

 6.3      Solve  :    2x-1 = 0 

 Add  1  to both sides of the equation : 
                      2x = 1
Divide both sides of the equation by 2:
                     x = 1/2 = 0.500

Two solutions were found :

1.  x = 1/2 = 0.500
   
2.  x = 0