Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.6" was replaced by "(6/10)".

Step  1  :

            3
 Simplify   —
            5

Equation at the end of step  1  :

    3                   
  ((— • x2) -  11x) -  10
    5                   

Step  2  :

Equation at the end of step  2  :

   3x2            
  (——— -  11x) -  10
    5             

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

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

           11x     11x • 5
    11x =  ———  =  ———————
            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:

 3x2 - (11x • 5)     3x2 - 55x
 ———————————————  =  —————————
        5                5    

Equation at the end of step  3  :

  (3x2 - 55x)    
  ——————————— -  10
       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 :

          10     10 • 5
    10 =  ——  =  ——————
          1        5   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   3x² - 55x  =   x • (3x - 55) 

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 x • (3x-55) - (10 • 5)     3x2 - 55x - 50
 ——————————————————————  =  ——————————————
           5                      5       

Trying to factor by splitting the middle term

 5.3     Factoring  3x² - 55x - 50 

The first term is,  3x²  its coefficient is  3 .
The middle term is,  -55x  its coefficient is  -55 .
The last term, "the constant", is  -50 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -50 = -150 

Step-2 : Find two factors of  -150  whose sum equals the coefficient of the middle term, which is   -55 .

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

Final result :

  3x2 - 55x - 50
  ——————————————
        5