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

Question

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

0

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