Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.2" was replaced by "(2/10)".

Step  1  :

            1
 Simplify   —
            5

Equation at the end of step  1  :

    1                   
  ((— • x2) +  40x) -  2500
    5                   

Step  2  :

Equation at the end of step  2  :

   x2            
  (—— +  40x) -  2500
   5             

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  5  as the denominator :

           40x     40x • 5
    40x =  ———  =  ———————
            1         5   

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 + 40x • 5     x2 + 200x
 ————————————  =  —————————
      5               5    

Equation at the end of step  3  :

  (x2 + 200x)    
  ——————————— -  2500
       5         

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

            2500     2500 • 5
    2500 =  ————  =  ————————
             1          5    

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   x² + 200x  =   x • (x + 200) 

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 x • (x+200) - (2500 • 5)     x2 + 200x - 12500
 ————————————————————————  =  —————————————————
            5                         5        

Trying to factor by splitting the middle term

 5.3     Factoring  x² + 200x - 12500 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +200x  its coefficient is  200 .
The last term, "the constant", is  -12500 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -12500 = -12500 

Step-2 : Find two factors of  -12500  whose sum equals the coefficient of the middle term, which is   200 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -50  and  250 
                     x² - 50x + 250x - 12500

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-50)
              Add up the last 2 terms, pulling out common factors :
                    250 • (x-50)
Step-5 : Add up the four terms of step 4 :
                    (x+250)  •  (x+50)
             Which is the desired factorization

Final result :

(x+250)  •  (x+50)