Answer
{$16,18$}
Work Step by Step
Step 1: Comparing $n^{2}-34n+288=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain:
$a=1$, $b=-34$, and $c=288$
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:
$x=\frac{-(-34) \pm \sqrt {(-34)^{2}-4(1)(288)}}{2(1)}$
Step 4: $x=\frac{34 \pm \sqrt {1156-1152}}{2}$
Step 5: $x=\frac{34 \pm \sqrt {4}}{2}$
Step 6: $x=\frac{34 \pm 2}{2}$
Step 7: $x=\frac{34+2}{2}$ or $x=\frac{34-2}{2}$
Step 8: $x=\frac{36}{2}$ or $x=\frac{32}{2}$
Step 9: $x=18$ or $x=16$
Step 10: Therefore, the solution set is {$16,18$}.
