Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.790457" was replaced by "(3790457/1000000)". 2 more similar replacement(s)

Step  1  :

            3790457
 Simplify   ———————
            1000000

Equation at the end of step  1  :

             255     3790457
  ((3•(x2))-(———•x))+———————
             100     1000000

Step  2  :

            51
 Simplify   ——
            20

Equation at the end of step  2  :

                  51          3790457
  ((3 • (x2)) -  (—— • x)) +  ———————
                  20          1000000
 Step  3  :

Equation at the end of step  3  :

          51x     3790457
  (3x2 -  ———) +  ———————
          20      1000000

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  20  as the denominator :

            3x2     3x2 • 20
     3x2 =  ———  =  ————————
             1         20   

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 :

 4.2       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 • 20 - (51x)     60x2 - 51x
 ————————————————  =  ——————————
        20                20    

Equation at the end of step  4  :

  (60x2 - 51x)    3790457
  ———————————— +  ———————
       20         1000000

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   60x² - 51x  =   3x • (20x - 17) 

Calculating the Least Common Multiple :

 6.2    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       1000000 

      Least Common Multiple:
      1000000 

Calculating Multipliers :

 6.3    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 50000

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 6.4      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.      3x • (20x-17) • 50000
   ——————————————————  =   —————————————————————
         L.C.M                    1000000       

   R. Mult. • R. Num.      3790457
   ——————————————————  =   ———————
         L.C.M             1000000

Adding fractions that have a common denominator :

 6.5       Adding up the two equivalent fractions

 3x • (20x-17) • 50000 + 3790457     3000000x2 - 2550000x + 3790457
 ———————————————————————————————  =  ——————————————————————————————
             1000000                            1000000            

Trying to factor by splitting the middle term

 6.6     Factoring  3000000x² - 2550000x + 3790457 

The first term is,  3000000x²  its coefficient is  3000000 .
The middle term is,  -2550000x  its coefficient is  -2550000 .
The last term, "the constant", is  +3790457 

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

Numbers too big. Method shall not be applied

Final result :

  3000000x2 + 2550000x + 3790457
  ——————————————————————————————
             1000000