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 :

                     x^23*x-(-4*x)=0 

Step by step solution :

Step  1  :

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   x²⁴ + 4x  =   x • (x²³ + 4) 

Equation at the end of step  2  :

  x • (x23 + 4)  = 0 

Step  3  :

Theory - Roots of a product :

 3.1    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 :

 3.2      Solve  :    x = 0 

  Solution is  x = 0

Solving a Single Variable Equation :

 3.3      Solve  :    x²³+4 = 0 

 Subtract  4  from both sides of the equation : 
                      x²³ = -4
                     x  =  23rd root of (-4) 

 Negative numbers have real 23th roots.
 23rd root of (-4) = ²³√ -1• 4  = ²³√ -1 • ²³√ 4  =(-1)•²³√ 4 

The equation has one real solution, a negative number This solution is  x = negative 23rd root of 4 = -1.0621

Two solutions were found :

1.  x = negative 23rd root of 4 = -1.0621
2.  x = 0