Answer
No real number solutions
Work Step by Step
Step 1: Comparing $n^{2}+6n+11=0$ to the standard form of a quadratic equation $an^{2}+bn+c=0$, we obtain:
$a=1$, $b=6$ and $c=11$
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:
$x=\frac{-(6) \pm \sqrt {(6)^{2}-4(1)(11)}}{2(1)}$
Step 4: $x=\frac{-6\pm \sqrt {36-44}}{2}$
Step 5: $x=\frac{-6 \pm \sqrt {-8}}{2}$
Since their are no real number solutions to $ \sqrt {-8}$, there are no real number solutions to the equation.
