Question

solve the equation using the quadratic formula
$x^2 + 9x + 6 = 0$
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 quadratic coefficients

For $ax^2+bx+c=0$, here $a=1$, $b=9$, $c=6$.

Step2: Recall quadratic formula

The formula is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$.

Step3: Calculate discriminant

$\Delta = b^2-4ac = 9^2-4(1)(6)=81-24=57$

Step4: Substitute into formula

$x=\frac{-9\pm\sqrt{57}}{2(1)}$

Answer:

$\frac{-9+\sqrt{57}}{2}, \frac{-9-\sqrt{57}}{2}$