x^2-15=0 Find the number of real number solutions for the equation.

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x^2-15=0 Find the number of real number solutions for the equation.

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    2021-09-06T02:19:42+00:00

     x2-15=0 Two solutions were found :                   x = ± √15 = ± 3.8730

    Step by step solution :Step  1  :Trying to factor as a Difference of Squares :

     1.1      Factoring:  x2-15 

    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 : 15 is not a square !! 

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

    Equation at the end of step  1  : x2 – 15 = 0
    Step  2  :Solving a Single Variable Equation :

     2.1      Solve  :    x2-15 = 0 

     Add  15  to both sides of the equation : 
     
                         x2 = 15 
     
     
    When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
     
                         x  =  ± √ 15  

     The equation has two real solutions  
     
    These solutions are  x = ± √15 = ± 3.8730  
     

    Two solutions were found :                   x = ± √15 = ± 3.8730

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