Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): ".0008" was replaced by "(0008/10000)".

Step  1  :

              1 
 Simplify   ————
            1250

Equation at the end of step  1  :

      1                    
  ((———— • x2) -  65x) +  220000
    1250                   

Step  2  :

Equation at the end of step  2  :

    x2             
  (———— -  65x) +  220000
   1250            

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  1250  as the denominator :

           65x     65x • 1250
    65x =  ———  =  ——————————
            1         1250   

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 - (65x • 1250)     x2 - 81250x
 —————————————————  =  ———————————
       1250               1250    

Equation at the end of step  3  :

  (x2 - 81250x)    
  ————————————— +  220000
      1250         

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  1250  as the denominator :

              220000     220000 • 1250
    220000 =  ——————  =  —————————————
                1            1250     

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   x² - 81250x  =   x • (x - 81250) 

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 x • (x-81250) + 220000 • 1250     x2 - 81250x + 275000000
 —————————————————————————————  =  ———————————————————————
             1250                           1250          

Trying to factor by splitting the middle term

 5.3     Factoring  x² - 81250x + 275000000 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -81250x  its coefficient is  -81250 .
The last term, "the constant", is  +275000000 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 275000000 = 275000000 

Step-2 : Find two factors of  275000000  whose sum equals the coefficient of the middle term, which is   -81250 .


Numbers too big. Method shall not be applied

Final result :

  x2 - 81250x + 275000000
  ———————————————————————
           1250