Use the models below to solve this equation [x] [x] 1/1 1/1 = 1 1/1

1.  x = 11

2.  x = -11

Step-by-step explanation:

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

                    (x)*(x)*1/11/1-(11/1)=0

                  11

Simplify   ——

                  1

             1

 (x2 • —— ÷ 1) - 11  = 0  

            11

                   1

Simplify   ——

                   11

            1          

 (x2 • —— ÷ 1) -  11  = 0  

            11        

               1      

Divide  ——  by  1

               11      

            1      

 (x2 • ——) -  11  = 0  

           11    

Subtracting a whole from a fraction

Rewrite the whole as a fraction using  11  as the denominator :

         11     11 • 11

   11 =  ——  =  ———————

         1        11    

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 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:

     x2 - (11 • 11)                                    x2 - 121

——————————————  =  ————————

            11                                              11          

   Factoring:  x2 - 121  

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 : 121 is the square of 11

Check :  x2  is the square of  x1  

Factorization is :       (x + 11)  •  (x - 11)  

             (x + 11) • (x - 11)

 ———————————————————  = 0  

                          11    

    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:

 (x+11)•(x-11)

 ————————————— • 11 = 0 • 11

      11      

Now, on the left hand side, the  11  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  (x+11)  •  (x-11)  = 0

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.

Solve  :    x+11 = 0  

Subtract  11  from both sides of the equation :  

                     x = -11

Solve  :    x-11 = 0  

Add  11  to both sides of the equation :  

                     x = 11

1.  x = 11

2.  x = -11

1.  x = 11

2.  x = -11

Step-by-step explanation:

1.  x = 11

2.  x = -11