Solve the equation using the quadratic formula. \[ x^{2}+5 x+3=0 \] The solution set is (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

To solve the quadratic equation \( x^{2} + 5x + 3 = 0 \) using the quadratic formula, follow these steps: The quadratic formula is: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] For the given equation: - \( a = 1 \) - \( b = 5 \) - \( c = 3 \) Plug these values into the formula: \[ x = \frac{-5 \pm \sqrt{5^2 - 4 \cdot 1 \cdot 3}}{2 \cdot 1} \] \[ x = \frac{-5 \pm \sqrt{25 - 12}}{2} \] \[ x = \frac{-5 \pm \sqrt{13}}{2} \] So, the solution set is: \[ \left\{ \frac{-5 + \sqrt{13}}{2}, \frac{-5 - \sqrt{13}}{2} \right\} \] **Final Answer:** \(\frac{-5+\sqrt{13}}{2}, \frac{-5-\sqrt{13}}{2}\)