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The solution to the equation \((2x - 1)^2 - 4(x - 2)(x + 2) = 0\) is:

\[
x = \frac{17}{4}
\]

Would you like more details about the steps involved? Here are some related questions to expand on this:

1. How do you expand and simplify expressions with squares and products?
2. What are the properties of the difference of squares used in this equation?
3. How do we factor quadratic equations?
4. Can you solve this equation using graphical methods?
5. How do you verify the solution of an equation?

**Tip:** Always check your solution by plugging it back into the original equation to ensure correctness!

This detailed solution walks through solving the quadratic equation (2x - 1)^2 - 4(x - 2)(x + 2) = 0. It covers expanding, simplifying expressions, and applying the difference of squares theorem. Suitable for students in Grades 9-12.

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