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

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