Find the values of k for which the equation x² - 6x + k = 0 has equal roots.

For equal roots, the discriminant must be zero: b² - 4ac = 0. Here (-6)² - 4(1)(k) = 0 gives 36 - 4k = 0, so k = 9. Choosing k = 36 is a common error from forgetting to divide by 4.