Question

solve the equation using the quadratic formula.
$x^2 + 11x + 9 = 0$

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.)

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 1\), \(b = 11\), \(c = 9\).

Step2: Apply quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Substitute values: \(x=\frac{-11\pm\sqrt{11^2 - 4(1)(9)}}{2(1)}\).

Step3: Simplify discriminant

Calculate \(b^2 - 4ac = 121 - 36 = 85\). So \(x=\frac{-11\pm\sqrt{85}}{2}\).

Answer:

\(\frac{-11 - \sqrt{85}}{2},\frac{-11 + \sqrt{85}}{2}\)