Solve the following equation by factorization:

4x² - 9x - 100 = 0, when x ∈ Q

Given,

⇒ 4x² - 9x - 100 = 0

⇒ 4x² + 16x - 25x - 100 = 0

⇒ 4x(x + 4) - 25(x + 4) = 0

⇒ (4x - 25)(x + 4) = 0

⇒ 4x - 25 = 0 or x + 4 = 0      [Using Zero-product rule]

⇒ 4x = 25 or x = -4

⇒ x = $\dfrac{25}{4}$ or x = -4

Since, x ∈ Q

Hence, x = $\Big{-4, \dfrac{25}{4}\Big}$.