Solve the equation using the quadratic formula. \[ x^{2}+11 \mathrm{x}+4=0 \] The solution set is (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed. Use in answers as needed.)
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To solve the equation \( x^{2}+11x+4=0 \) using the quadratic formula, we use: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = 1 \), \( b = 11 \), and \( c = 4 \). Plugging these values into the formula: 1. Calculate the discriminant: \[ b^2 - 4ac = 11^2 - 4 \cdot 1 \cdot 4 = 121 - 16 = 105 \] 2. Now, substitute back into the formula: \[ x = \frac{-11 \pm \sqrt{105}}{2 \cdot 1} = \frac{-11 \pm \sqrt{105}}{2} \] Thus, the solution set is: \[ x = \frac{-11 + \sqrt{105}}{2} \quad \text{and} \quad x = \frac{-11 - \sqrt{105}}{2} \]
