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

Question

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## Answers ( No )

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