Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2". 

Rearrange:

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

                     2*x^2-19*x^2-(-10*x)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  ((2 • (x2)) -  19x2) -  -10x  = 0 
 Step  2  :

Equation at the end of step  2  :

  (2x2 -  19x2) -  -10x  = 0 

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   10x - 17x²  =   -x • (17x - 10) 

Equation at the end of step  4  :

  -x • (17x - 10)  = 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  :    -x = 0 

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

Solving a Single Variable Equation :

 5.3      Solve  :    17x-10 = 0 

 Add  10  to both sides of the equation : 
                      17x = 10
Divide both sides of the equation by 17:
                     x = 10/17 = 0.588

Two solutions were found :

1.  x = 10/17 = 0.588
   
2.  x = 0