1. **State the problem:** Solve the quadratic equation $$4q^2 + q + 1 = -3q$$ using the quadratic formula. 2. **Rewrite the equation in standard form:** Move all terms to one side: $$4q^2 + q + 1 + 3q = 0$$ $$4q^2 + 4q + 1 = 0$$ 3. **Identify coefficients:** $$a = 4, \quad b = 4, \quad c = 1$$ 4. **Recall the quadratic formula:** $$q = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 5. **Calculate the discriminant:** $$b^2 - 4ac = 4^2 - 4 \times 4 \times 1 = 16 - 16 = 0$$ 6. **Since the discriminant is zero, there is one real repeated root:** 7. **Apply the quadratic formula:** $$q = \frac{-4 \pm \sqrt{0}}{2 \times 4} = \frac{-4 \pm 0}{8}$$ 8. **Simplify:** $$q = \frac{-4}{8} = -\frac{1}{2}$$ **Final answer:** $$q = -\frac{1}{2}$$