Solve by Factoring x^2-25=0

Problem

x2−25=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 25 as 5 to clearly see the squares.

x2−5=0

3. Factor the expression using the difference of squares formula where a=x and b=5

(x−5)*(x+5)=0

4. Apply the zero product property, which states that if the product of two factors is zero, at least one of the factors must be zero.

x−5=0

x+5=0

5. Solve each linear equation for x by isolating the variable.

x=5

x=−5

Final Answer

x=5,−5

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