83.2k views
2 votes
X^2-15=0 Find the number of real number solutions for the equation.

1 Answer

2 votes
x2-15=0 Two solutions were found : x = ± √15 = ± 3.8730Step 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
User Choxx
by
6.2k points