Solve the following equation using the quadratic formula. \( x^{2}+13 x+7=0 \) The solution set is \( \{ \) \}. (Simplify your answer, including any radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Solve the equation \( x^{2}+13x+7=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(x^{2}+13x+7=0\) - step1: Solve using the quadratic formula: \(x=\frac{-13\pm \sqrt{13^{2}-4\times 7}}{2}\) - step2: Simplify the expression: \(x=\frac{-13\pm \sqrt{141}}{2}\) - step3: Separate into possible cases: \(\begin{align}&x=\frac{-13+\sqrt{141}}{2}\\&x=\frac{-13-\sqrt{141}}{2}\end{align}\) - step4: Rewrite the fraction: \(\begin{align}&x=\frac{-13+\sqrt{141}}{2}\\&x=-\frac{13+\sqrt{141}}{2}\end{align}\) - step5: Rewrite: \(x_{1}=-\frac{13+\sqrt{141}}{2},x_{2}=\frac{-13+\sqrt{141}}{2}\) The solutions to the equation \(x^{2}+13x+7=0\) using the quadratic formula are \(x_{1}=-\frac{13+\sqrt{141}}{2}\) and \(x_{2}=\frac{-13+\sqrt{141}}{2}\).