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2 August, 10:55

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

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  1. 2 August, 11:01
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    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
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