Solution - Linear equations with one unknown

Rearrange:

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

                     16*x-(28*x^48)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  16x -  (22•7x48)  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   16x - 28x⁴⁸  =   -4x • (7x⁴⁷ - 4) 

Equation at the end of step  3  :

  -4x • (7x47 - 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  :    -4x = 0 

 Multiply both sides of the equation by (-1) :  4x = 0


Divide both sides of the equation by 4:
                     x = 0

Solving a Single Variable Equation :

 4.3      Solve  :    7x⁴⁷-4 = 0 

 Add  4  to both sides of the equation : 
                      7x⁴⁷ = 4
Divide both sides of the equation by 7:
                     x⁴⁷ = 4/7 = 0.571
                     x  =  47th root of (4/7) 

 The equation has one real solution
This solution is  x = 47th root of ( 0.571) = 0.98816

Two solutions were found :

1.  x = 47th root of ( 0.571) = 0.98816
2.  x = 0