Question

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

Answer 1

 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