Solution - Factoring binomials using the difference of squares

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2". 

Rearrange:

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

                     289-(x^2)=0 

Step by step solution :

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  289-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 :  289  is the square of  17 
Check :  x²  is the square of  x¹ 

Factorization is :       (17 + x)  •  (17 - x) 

Equation at the end of step  1  :

  (x + 17) • (17 - x)  = 0 

Step  2  :

Theory - Roots of a product :

 2.1    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.

Solving a Single Variable Equation :

 2.2      Solve  :    x+17 = 0 

 Subtract  17  from both sides of the equation : 
                      x = -17

Solving a Single Variable Equation :

 2.3      Solve  :    -x+17 = 0 

 Subtract  17  from both sides of the equation : 
                      -x = -17
Multiply both sides of the equation by (-1) :  x = 17

Two solutions were found :

1.  x = 17
   
2.  x = -17