Solve by Factoring 4w^2-25=0

Problem

4*w^2−25=0

Solution

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

2. Determine the values of a and b by taking the square roots of the terms: a=√(,4*w^2)=2*w and b=√(,25)=5

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

(2*w−5)*(2*w+5)=0

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

2*w−5=0

2*w+5=0

5. Solve each linear equation for w

2*w=5⇒w=5/2

2*w=−5⇒w=−5/2

Final Answer

w=±5/2

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