If $(64)^2 - (36)^2 = 20 \times x$, then $x =$

### Concept & Formula Apply the difference of two perfect squares formula to the left side of the equation to simplify the large numbers without resorting to manual squaring. $$a^2 - b^2 = (a - b)(a + b)$$ ### Step-by-Step Solution * **Given:** $(64)^2 - (36)^2 = 20x$ * Focus on the left side of the equation and apply the difference of squares identity where $a = 64$ and $b = 36$: $$(64 - 36)(64 + 36) = 20x$$ * Perform the basic subtraction and addition inside the parentheses: $$(28)(100) = 20x$$ * Multiply the terms to simplify the left side completely: $$2800 = 20x$$ * Divide both sides by 20 to isolate and solve for $x$: $$x = \frac{2800}{20}$$ $$x = 140$$ ### Exam Strategy & Shortcut You can skip full multiplication by manipulating the factors directly. Once you reach $(28)(100) = 20x$, simply divide 100 by 20 in your head to get 5. Then, calculate $28 \times 5 = 140$. This eliminates the intermediate step of dealing with 2800, minimizing trailing zeros and saving a few extra seconds. ### Common Pitfall Manually squaring 64 ($4096$) and 36 ($1296$) before subtracting is the most common error. While mathematically sound, it introduces massive potential for calculation mistakes and consumes precious time compared to algebraic factoring. ### Final Answer Therefore, the correct answer is **140**.