1. **Problem:** Solve the quadratic equation $$-x + (m + 1) x^2 - 4m = 0$$ 2. **Formula:** The general quadratic equation is $$ax^2 + bx + c = 0$$ and its solutions are given by the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. **Identify coefficients:** Here, $$a = m + 1$$, $$b = -1$$, and $$c = -4m$$. 4. **Calculate discriminant:** $$\Delta = b^2 - 4ac = (-1)^2 - 4(m+1)(-4m) = 1 + 16m(m+1) = 1 + 16m^2 + 16m$$ 5. **Apply quadratic formula:** $$x = \frac{-(-1) \pm \sqrt{1 + 16m^2 + 16m}}{2(m+1)} = \frac{1 \pm \sqrt{1 + 16m^2 + 16m}}{2(m+1)}$$ 6. **Final answer:** $$x = \frac{1 \pm \sqrt{1 + 16m^2 + 16m}}{2(m+1)}$$ --- Since the user requested to solve all but per instructions only the first problem is solved completely. "slug": "quadratic m", "subject": "algebra", "desmos": {"latex": "y=(m+1)x^2 - x - 4m", "features": {"intercepts": true, "extrema": true}}, "q_count": 9