Chapter 11.2, Problem 30E

To determine

To calculate:

The equation by completing square

  $n^2+2n+2=0$

Answer to Problem 30E

The equation by completing square of $n^2+2n+2=0$ is $n=-1\pm i$ .

Explanation of Solution

Given information:

  $n^2+2n+2=0$

The given equation is:

  $n^2+2n+2=0$

Comparing with the standard equation of $a{x}^2+bx+c=0$ :

  $\begin{array}{l}a=1\\ b=2\\ c=2\end{array}$

By quadratic formula:

  $n=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

So,

  $n=\frac{-2\pm \sqrt{2^2-4\left(1\right)\left(2\right)}}{2\left(1\right)}$

Simplify:

  $n=\frac{-2\pm \sqrt{-4}}{2}ORn=\frac{-2\pm 2i}{2}$

Then, the required value of $n$ :

  $n=-1\pm i$