Solve by Factoring x^2-49=0

Problem

x^2−49=0

Solution

1. Identify the expression on the left side as a difference of squares, which follows the pattern a^2−b^2=(a−b)*(a+b)

2. Rewrite the constant 49 as 7^2 to clearly see the squares.

3. Factor the expression x^2−7^2 into (x−7)*(x+7)

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

5. Solve the resulting linear equations x−7=0 and x+7=0

Final Answer

x=7,−7

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