Answer
{$-14,-13$}
Work Step by Step
Step 1: Comparing $n^{2}+27n+182=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain:
$a=1$, $b=27$, and $c=182$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a,b, and c in the formula, we obtain:
$x=\frac{-(27) \pm \sqrt {(27)^{2}-4(1)(182)}}{2(1)}$
Step 4: $x=\frac{-27 \pm \sqrt {729-728}}{2}$
Step 5: $x=\frac{-27 \pm \sqrt {1}}{2}$
Step 6: $x=\frac{-27 \pm 1}{2}$
Step 7: $x=\frac{-27+1}{2}$ or $x=\frac{-27-1}{2}$
Step 8: $x=\frac{-26}{2}$ or $x=\frac{-28}{2}$
Step 9: $x=-13$ or $x=-14$
Step 10: Therefore, the solution set is {$-14,-13$}.
