Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.25" was replaced by "(625/100)".

Step  1  :

            25
 Simplify   ——
            4 

Equation at the end of step  1  :

            25            
  (125x -  (—— • x2)) -  465
            4             

Step  2  :

Equation at the end of step  2  :

           25x2     
  (125x -  ————) -  465
            4       

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  4  as the denominator :

             125x     125x • 4
     125x =  ————  =  ————————
              1          4    

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:

 125x • 4 - (25x2)     500x - 25x2
 —————————————————  =  ———————————
         4                  4     

Equation at the end of step  3  :

  (500x - 25x2)    
  ————————————— -  465
        4          

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

           465     465 • 4
    465 =  ———  =  ———————
            1         4   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   500x - 25x²  =   -25x • (x - 20) 

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 -25x • (x-20) - (465 • 4)     -25x2 + 500x - 1860
 —————————————————————————  =  ———————————————————
             4                          4         

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -25x² + 500x - 1860  =   -5 • (5x² - 100x + 372) 

Trying to factor by splitting the middle term

 6.2     Factoring  5x² - 100x + 372 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  -100x  its coefficient is  -100 .
The last term, "the constant", is  +372 

Step-1 : Multiply the coefficient of the first term by the constant   5 • 372 = 1860 

Step-2 : Find two factors of  1860  whose sum equals the coefficient of the middle term, which is   -100 .

For tidiness, printing of 42 lines which failed to find two such factors, was suppressed

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

Final result :

  -5 • (5x2 - 100x + 372)
  ———————————————————————
             4