1. **State the problem:** Solve the quadratic equation $x^2 + 5x + 3 = 0$ and find solutions correct to 2 decimal places. 2. **Formula used:** The quadratic formula for solving $ax^2 + bx + c = 0$ is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=5$, and $c=3$. 3. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 5^2 - 4 \times 1 \times 3 = 25 - 12 = 13$$ Since $\Delta > 0$, there are two distinct real roots. 4. **Find the roots:** $$x = \frac{-5 \pm \sqrt{13}}{2}$$ Calculate $\sqrt{13} \approx 3.60555$. 5. **Evaluate each root:** - First root: $$x_1 = \frac{-5 + 3.60555}{2} = \frac{-1.39445}{2} = -0.69722 \approx -0.70$$ - Second root: $$x_2 = \frac{-5 - 3.60555}{2} = \frac{-8.60555}{2} = -4.30278 \approx -4.30$$ 6. **Final answer:** The solutions to $x^2 + 5x + 3 = 0$ correct to 2 decimal places are $$x \approx -0.70 \text{ and } x \approx -4.30$$