Solution - Factoring binomials using the difference of squares

Rearrange:

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

                     4-2*a^2-(-7)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (4 -  2a2) -  -7  = 0 

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  11-2a² 

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 :  11  is not a square !!

Ruling : Binomial can not be factored as the
difference of two perfect squares

Equation at the end of step  2  :

  11 - 2a2  = 0 

Step  3  :

Solving a Single Variable Equation :

 3.1      Solve  :    -2a²+11 = 0 

 Subtract  11  from both sides of the equation : 
                      -2a² = -11
Multiply both sides of the equation by (-1) :  2a² = 11


Divide both sides of the equation by 2:
                     a² = 11/2 = 5.500
 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      a  =  ± √ 11/2  

 The equation has two real solutions  
 These solutions are  a = ±√ 5.500 = ± 2.34521  
 

Two solutions were found :