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Rearrange:

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

                (x-2)^2/25+(y-3)^2/49-(1)=0 

Step  1  :

            (y - 3)2
 Simplify   ————————
               49   

Equation at the end of step  1  :

   ((x - 2)2)    (y - 3)2     
  (—————————— +  ————————) -  1  = 0 
       25           49        

Step  2  :

            (x - 2)2
 Simplify   ————————
               25   

Equation at the end of step  2  :

   (x - 2)2    (y - 3)2     
  (———————— +  ————————) -  1  = 0 
      25          49        

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       25 

      The right denominator is :       49 

      Least Common Multiple:
      1225 

Calculating Multipliers :

 3.2    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 = 49

   Right_M = L.C.M / R_Deno = 25

Making Equivalent Fractions :

 3.3      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.      (x-2)2 • 49
   ——————————————————  =   ———————————
         L.C.M                1225    

   R. Mult. • R. Num.      (y-3)2 • 25
   ——————————————————  =   ———————————
         L.C.M                1225    

Adding fractions that have a common denominator :

 3.4       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:

 (x-2)2 • 49 + (y-3)2 • 25     49x2 - 196x + 25y2 - 150y + 421
 —————————————————————————  =  ———————————————————————————————
           1225                             1225              

Equation at the end of step  3  :

  (49x2 - 196x + 25y2 - 150y + 421)    
  ————————————————————————————————— -  1  = 0 
                1225                   

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  1225  as the denominator :

         1     1 • 1225
    1 =  —  =  ————————
         1       1225  

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

 (49x2-196x+25y2-150y+421) - (1225)     49x2 - 196x + 25y2 - 150y - 804
 ——————————————————————————————————  =  ———————————————————————————————
                1225                                 1225              

Equation at the end of step  4  :

  49x2 - 196x + 25y2 - 150y - 804
  ———————————————————————————————  = 0 
               1225              

Step  5  :

When a fraction equals zero :

 5.1    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:

  49x2-196x+25y2-150y-804
  ——————————————————————— • 1225 = 0 • 1225
           1225          

Now, on the left hand side, the  1225  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   49x²-196x+25y²-150y-804  = 0

Solving a Single Variable Equation :

 5.2     Solve   49x²-196x+25y²-150y-804  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

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