1. Solve the quadratic equation $x^2 + 6x + 4 = 0$. Use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a=1$, $b=6$, $c=4$. Calculate discriminant $\Delta = 6^2 - 4(1)(4) = 36 - 16 = 20$. Find roots $x = \frac{-6 \pm \sqrt{20}}{2} = \frac{-6 \pm 2\sqrt{5}}{2} = -3 \pm \sqrt{5}$. 2. Solve $2x^2 + 10x + 45 = 29$. Rewrite as $2x^2 + 10x + 45 - 29 = 0 \Rightarrow 2x^2 + 10x + 16 = 0$. Divide by 2: $x^2 + 5x + 8 = 0$. Calculate discriminant $\Delta = 5^2 - 4(1)(8) = 25 - 32 = -7$ (negative discriminant). No real solutions; roots are complex: $x = \frac{-5 \pm i\sqrt{7}}{2}$. 3. Solve $x^2 - 16x + 20 = -8$. Rewrite as $x^2 - 16x + 20 + 8 = 0 \Rightarrow x^2 - 16x + 28 = 0$. Calculate discriminant $\Delta = (-16)^2 - 4(1)(28) = 256 - 112 = 144$. Roots: $x = \frac{16 \pm 12}{2}$. Hence $x = 14$ or $x = 2$. 4. Solve $4x^2 + 32x - 64 = 0$. Divide entire equation by 4: $x^2 + 8x - 16 = 0$. Discriminant $\Delta = 8^2 - 4(1)(-16) = 64 + 64 = 128$. Roots: $x = \frac{-8 \pm \sqrt{128}}{2} = \frac{-8 \pm 8\sqrt{2}}{2} = -4 \pm 4\sqrt{2}$. 5. Solve $x^2 - 25x + 3x - 121 = 22x$. Combine like terms: $x^2 - 22x - 121 = 22x$. Bring all terms to one side: $x^2 - 22x - 121 - 22x = 0 \Rightarrow x^2 - 44x - 121 = 0$. Discriminant $\Delta = (-44)^2 - 4(1)(-121) = 1936 + 484 = 2420$. Roots: $x = \frac{44 \pm \sqrt{2420}}{2} = 22 \pm \sqrt{605}$. 6. Solve $x^2 + 67x = 0$. Factor: $x(x + 67) = 0$. Solutions: $x = 0$ or $x = -67$. 7. Solve $x^2 + 45x = -46$. Rewrite: $x^2 + 45x + 46 = 0$. Discriminant $\Delta = 45^2 - 4(1)(46) = 2025 - 184 = 1841$. Roots: $x = \frac{-45 \pm \sqrt{1841}}{2}$. 8. Solve $2x^2 + 25 = 26x$. Bring all to one side: $2x^2 - 26x + 25 = 0$. Discriminant $\Delta = (-26)^2 - 4(2)(25) = 676 - 200 = 476$. Roots: $x = \frac{26 \pm \sqrt{476}}{4}$. II. Use annuity formulas to solve the problems. 1. Robert: $P=4000$ (monthly), $r=5\% = 0.05$ annually, $t=36$ years 4 months = $36 + \frac{4}{12} = 36.3333$ years. Monthly interest rate $i = \frac{0.05}{12} \approx 0.0041667$. Number of payments $n = 36.3333 \times 12 = 436$. Future Value (FV) formula: $$FV = P \times \frac{(1+i)^n - 1}{i}$$ Calculate: $$FV = 4000 \times \frac{(1.0041667)^{436} - 1}{0.0041667}$$. Present Value (PV) formula: $$PV = P \times \frac{1 - (1+i)^{-n}}{i}$$ Calculate: $$PV = 4000 \times \frac{1 - (1.0041667)^{-436}}{0.0041667}$$. 2. Philip: $P=300$, $r=6.5\% = 0.065$ annually, $t=16$ years. Monthly interest rate $i = \frac{0.065}{12} \approx 0.0054167$. Number of payments $n = 16 \times 12 = 192$. Future Value (FV): $$FV = 300 \times \frac{(1.0054167)^{192} - 1}{0.0054167}$$. Present Value (PV): $$PV = 300 \times \frac{1 - (1.0054167)^{-192}}{0.0054167}$$. III. Missing values refer to previous questions or annuity amounts; if any specific missing is required, please specify.