Chapter 4.6, Problem 2AYU

To determine

To calculate:

The complex solution of the given equation is to be estimated:

  $x^2+2x+2$

Answer to Problem 2AYU

The complex solution of the given equation is $-1\pm i$ .

Explanation of Solution

Given information:

  $x^2+2x+2$

Formula Used:

The solution of the quadratic equation $a{x}^2+bx+c$ is expressed as:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

The given equation is:

  $x^2+2x+2$

Compare it with the standard quadratic equation $a{x}^2+bx+c$ :

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

The complex solutions of the given equation are:

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-2\pm \sqrt{{\left(2\right)}^2-\left(4\times 1\times 2\right)}}{2\times 1}\\ x=\frac{-2\pm \sqrt{4-8}}{2}\\ x=\frac{-2\pm \sqrt{-4}}{2}\\ x=\frac{-2\pm i\sqrt{4}}{2}\left[\because \sqrt{-1}=i\right]\\ x=-1\pm i\end{array}$

Hence, the solutions are $x=-1+i,-1-i$ .