Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): ".0005" was replaced by "(0005/10000)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                250000-(((5/10000)*x)*50*x)=0 

Step by step solution :

Step  1  :

              1 
 Simplify   ————
            2000

Equation at the end of step  1  :

                 1 
  250000 -  (((———— • x) • 50) • x)  = 0 
               2000
 Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  40  as the denominator :

               250000     250000 • 40
     250000 =  ——————  =  ———————————
                 1            40     

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 :

 2.2       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:

 250000 • 40 - (x2)     10000000 - x2
 ——————————————————  =  —————————————
         40                  40      

Trying to factor as a Difference of Squares :

 2.3      Factoring:  10000000 - x² 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  10000000  is not a square !!

Ruling : Binomial can not be factored as the
difference of two perfect squares

Equation at the end of step  2  :

  10000000 - x2
  —————————————  = 0 
       40      

Step  3  :

When a fraction equals zero :

 3.1    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:

  10000000-x2
  ——————————— • 40 = 0 • 40
      40     

Now, on the left hand side, the  40  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   10000000-x²  = 0

Solving a Single Variable Equation :

 3.2      Solve  :    -x²+10000000 = 0 

 Subtract  10000000  from both sides of the equation : 
                      -x² = -10000000
Multiply both sides of the equation by (-1) :  x² = 10000000


 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      x  =  ± √ 10000000  

 Can  √ 10000000 be simplified ?

Yes!   The prime factorization of  10000000   is
   2•2•2•2•2•2•2•5•5•5•5•5•5•5 
To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 10000000   =  √ 2•2•2•2•2•2•2•5•5•5•5•5•5•5   =2•2•2•5•5•5•√ 10   =
                ±  1000 • √ 10

The equation has two real solutions  
 These solutions are  x = 1000 • ± √10 = ± 3162.2777  
 

Two solutions were found :