If 64² − 36² = 20 × x, find the value of x.

Problem Restatement

Use the difference-of-squares identity to evaluate 64² − 36² and solve for x in 20x.

Concept / Approach

(A² − B²) = (A − B)(A + B).

Step-by-Step Calculation

64² − 36² = (64 − 36)(64 + 36) = 28 × 100 = 28002800 = 20x → x = 2800 ÷ 20 = 140

Final Answer

140