Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.03" was replaced by "(03/100)".

Rearrange:

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

                12000-(x*(1+(3/100)/2)^6)=0 

Step by step solution :

Step  1  :

             3 
 Simplify   ———
            100

Equation at the end of step  1  :

                        3 
  12000 -  (x • ((1 +  ——— ÷ 2)6))  = 0 
                       100

Step  2  :

          3       
 Divide  ———  by  2
         100      

Equation at the end of step  2  :

                        3 
  12000 -  (x • ((1 +  ———)6))  = 0 
                       200

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  200  as the denominator :

          1     1 • 200
     1 =  —  =  ———————
          1       200  

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:

 200 + 3     203
 ———————  =  ———
   200       200

Equation at the end of step  3  :

                 203
  12000 -  (x • (———)6))  = 0 
                 200

Step  4  :

 4.1     203 = 7•29

(203)⁶ = (7•29)⁶ = 7⁶ • 29⁶  4.2     200 = 2³•5² (200)⁶ = (2³•5²)⁶ = 2¹⁸ • 5¹²

Equation at the end of step  4  :

                 (76•296)
  12000 -  (x • —————————)  = 0 
                (218•512)

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2¹⁸ • 5¹²  as the denominator :

              12000     12000 • (218•512)
     12000 =  —————  =  —————————————————
                1           (218•512)    

Calculating Multipliers :

 5.2    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 = 2¹⁸ • 5¹²

   Right_M = L.C.M / R_Deno = 1

Adding fractions that have a common denominator :

 5.3       Adding up the two equivalent fractions

Multiplying exponents :

 2⁵  multiplied by  2¹⁸   = 2^{(5 + 18)} = 2²³

Multiplying exponents :

 5³  multiplied by  5¹²   = 5^{(3 + 12)} = 5¹⁵ 12000 • (2¹⁸•5¹²) - ((7⁶•29⁶x)) -7⁶•29⁶x + 2²³•3•5¹⁵ ——————————————————————————————— = ———————————————————— (2¹⁸•5¹²) 1

Equation at the end of step  5  :

  0 + 12000
  —————————  = 0 
      1    

Step  6  :

When a fraction equals zero :

 6.1    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:

  0+12000
  ——————— • 1 = 0 • 1
     1   

Now, on the left hand side, the  1  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   0+12000  = 0

Solving a Single Variable Equation :

 6.2      Solve  :    0+12000 = 0 

 Subtract  12000  from both sides of the equation : 
                      -12000 = -12000
Multiply both sides of the equation by (-1) :  12000 = 12000


Divide both sides of the equation by 12000:
                     1 = 1
                     1x  =  √ 1  

 The equation has one real solution
This solution is  1x =

One solution was found :