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Step by Step Solution

Rearrange:

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

e/16*x^2+25*y^2-(1600)=0

Step 1 :

Equation at the end of step 1 :

     e                        
  ((—— • (x²)) +  5²y²) -  1600  = 0 
    16                        
 Step  2  :
             e
 Simplify   ——
            16

Equation at the end of step 2 :

     e                      
  ((—— • x²) +  5²y²) -  1600  = 0 
    16

Step 3 :

Equation at the end of step 3 :

   ex²               
  (——— +  5²y²) -  1600  = 0 
   16

Step 4 :

Rewriting the whole as an Equivalent Fraction :

4.1 Adding a whole to a fraction

Rewrite the whole as a fraction using 16 as the denominator :

            5²y²     5²y² • 16
    5²y² =  ————  =  —————————
             1          16

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:

 ex² + 5²y² • 16      ex² + 400y²
 ———————————————  =  ———————————
       16                16

Equation at the end of step 4 :

  (ex² + 400y²)    
  ————————————— -  1600  = 0 
       16

Step 5 :

Rewriting the whole as an Equivalent Fraction :

5.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 16 as the denominator :

            1600     1600 • 16
    1600 =  ————  =  —————————
             1          16

Adding fractions that have a common denominator :

5.2 Adding up the two equivalent fractions

 (ex²+400y²) - (1600 • 16)     ex² + 400y² - 25600
 —————————————————————————  =  ———————————————————
            16                         16

Trying to factor a multi variable polynomial :

5.3 Factoring ex² + 400y² - 25600

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Equation at the end of step 5 :

  ex² + 400y² - 25600
  ———————————————————  = 0 
          16

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:

  ex²+400y²-25600
  ——————————————— • 16 = 0 • 16
        16

Now, on the left hand side, the 16 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
ex²+400y²-25600 = 0

Solving a Single Variable Equation :

6.2 Solve ex²+400y²-25600 = 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.