Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.5" was replaced by "(5/10)".

Step by step solution :

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

          1                      
  ((0 -  (— • p2)) +  1900p) -  1200000  = 0 
          2                      

Step  2  :

Equation at the end of step  2  :

         p2               
  ((0 -  ——) +  1900p) -  1200000  = 0 
         2                

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

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

             1900p     1900p • 2
    1900p =  —————  =  —————————
               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:

 -p2 + 1900p • 2     3800p - p2
 ———————————————  =  ——————————
        2                2     

Equation at the end of step  3  :

  (3800p - p2)    
  ———————————— -  1200000  = 0 
       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 :

               1200000     1200000 • 2
    1200000 =  ———————  =  ———————————
                  1             2     

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   3800p - p²  =   -p • (p - 3800) 

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 -p • (p-3800) - (1200000 • 2)     -p2 + 3800p - 2400000
 —————————————————————————————  =  —————————————————————
               2                             2          

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -p² + 3800p - 2400000  =   -1 • (p² - 3800p + 2400000) 

Trying to factor by splitting the middle term

 6.2     Factoring  p² - 3800p + 2400000 

The first term is,  p²  its coefficient is  1 .
The middle term is,  -3800p  its coefficient is  -3800 .
The last term, "the constant", is  +2400000 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 2400000 = 2400000 

Step-2 : Find two factors of  2400000  whose sum equals the coefficient of the middle term, which is   -3800 .


Numbers too big. Method shall not be applied

Equation at the end of step  6  :

  (800 - p) • (p - 3000)
  ——————————————————————  = 0 
            2           

Step  7  :

When a fraction equals zero :

 7.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

  (800-p)•(p-3000)
  ———————————————— • 2 = 0 • 2
         2        

Now, on the left hand side, the  2  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   (800-p)  •  (p-3000)  = 0

Theory - Roots of a product :

 7.2    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

 7.3      Solve  :    -p+800 = 0 

 Subtract  800  from both sides of the equation : 
                      -p = -800
Multiply both sides of the equation by (-1) :  p = 800

Solving a Single Variable Equation :

 7.4      Solve  :    p-3000 = 0 

 Add  3000  to both sides of the equation : 
                      p = 3000

Two solutions were found :

1.  p = 3000
2.  p = 800