Solve by Factoring x^2-9=0

Problem

x2−9=0

Solution

1. Identify the expression on the left side as a difference of squares, which follows the pattern a2−b2=(a−b)*(a+b)

2. Rewrite the constant 9 as 3 to clearly see the squares.

x2−3=0

3. Factor the left side using the difference of squares formula.

(x−3)*(x+3)=0

4. Apply the zero product property by setting each individual factor equal to zero.

x−3=0

x+3=0

5. Solve each linear equation for x

x=3

x=−3

Final Answer

x=±3

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