Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x1"   was replaced by   "x^1".  1 more similar replacement(s).

Rearrange:

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

                     -5*x^2-x^56-(x^15)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  ((0 -  5x2) -  x56) -  x15  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -x⁵⁶ - x¹⁵ - 5x²  =   -x² • (x⁵⁴ + x¹³ + 5) 

Equation at the end of step  3  :

  -x2 • (x54 + x13 + 5)  = 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  :    -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

Equations of order 5 or higher :

 4.3     Solve   x⁵⁴+x¹³+5 = 0

Handling of functions of an even degree greater than 6 is not implemented yet

One solution was found :