Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.05" was replaced by "(05/100)".

Step  1  :

             1
 Simplify   ——
            20

Equation at the end of step  1  :

     1                 
  ((—— • x2) +  x) -  1
    20                 

Step  2  :

Equation at the end of step  2  :

   x2          
  (—— +  x) -  1
   20          

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  20  as the denominator :

         x     x • 20
    x =  —  =  ——————
         1       20  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 x2 + x • 20     x2 + 20x
 ———————————  =  ————————
     20             20   

Equation at the end of step  3  :

  (x2 + 20x)    
  —————————— -  1
      20        

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  20  as the denominator :

         1     1 • 20
    1 =  —  =  ——————
         1       20  

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   x² + 20x  =   x • (x + 20) 

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 x • (x+20) - (20)     x2 + 20x - 20
 —————————————————  =  —————————————
        20                  20      

Trying to factor by splitting the middle term

 5.3     Factoring  x² + 20x - 20 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +20x  its coefficient is  20 .
The last term, "the constant", is  -20 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -20 = -20 

Step-2 : Find two factors of  -20  whose sum equals the coefficient of the middle term, which is   20 .

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  x2 + 20x + 20
  —————————————
       20