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 :

                     1-(10*x^2)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  1 -  (2•5x2)  = 0 

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  1-10x² 

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 :  1  is the square of  1 
Check : 10 is not a square !!

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

Equation at the end of step  2  :

  1 - 10x2  = 0 

Step  3  :

Solving a Single Variable Equation :

 3.1      Solve  :    -10x²+1 = 0 

 Subtract  1  from both sides of the equation : 
                      -10x² = -1
Multiply both sides of the equation by (-1) :  10x² = 1


Divide both sides of the equation by 10:
                     x² = 1/10 = 0.100
 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      x  =  ± √ 1/10  

 The equation has two real solutions  
 These solutions are  x = ±√ 0.100 = ± 0.31623  
 

Two solutions were found :