Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.5" was replaced by "(25/10)".

Step  1  :

            5
 Simplify   —
            2

Equation at the end of step  1  :

    5                  
  ((— • x2) -  2x) -  65
    2                  

Step  2  :

Equation at the end of step  2  :

   5x2           
  (——— -  2x) -  65
    2            

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  2  as the denominator :

          2x     2x • 2
    2x =  ——  =  ——————
          1        2   

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:

 5x2 - (2x • 2)     5x2 - 4x
 ——————————————  =  ————————
       2               2    

Equation at the end of step  3  :

  (5x2 - 4x)    
  —————————— -  65
      2         

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  2  as the denominator :

          65     65 • 2
    65 =  ——  =  ——————
          1        2   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   5x² - 4x  =   x • (5x - 4) 

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 x • (5x-4) - (65 • 2)     5x2 - 4x - 130
 —————————————————————  =  ——————————————
           2                     2       

Trying to factor by splitting the middle term

 5.3     Factoring  5x² - 4x - 130 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  -4x  its coefficient is  -4 .
The last term, "the constant", is  -130 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -130 = -650 

Step-2 : Find two factors of  -650  whose sum equals the coefficient of the middle term, which is   -4 .

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

Final result :

  5x2 - 4x - 130
  ——————————————
        2