Solve the following equation:

4x² + 4x + 1 = 0

Given, 4x² + 4x + 1 = 0.

⇒ 4x² + 2x + 2x + 1 = 0

⇒ 2x(2x + 1) + 1(2x + 1) = 0

⇒ (2x + 1)(2x + 1) = 0

⇒ (2x + 1)² = 0

⇒ 2x + 1 = 0 or 2x + 1 = 0

⇒ 2x = -1 or 2x = -1

⇒ x = $-\dfrac{1}{2}, -\dfrac{1}{2}$.

Hence, roots of the given equations are $-\dfrac{1}{2}, -\dfrac{1}{2}$