Solve by Factoring x^2-64=0

Problem

x2−64=0

Solution

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

2. Rewrite the constant term as a square, noting that 64=8

3. Factor the quadratic expression using the difference of squares formula.

x2−8=0

(x−8)*(x+8)=0

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

x−8=0

x+8=0

5. Solve each linear equation for x

x=8

x=−8

Final Answer

x=±8

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