Chapter 11.2, Problem 29E

To determine

To calculate:

The equation by completing square

  $s^2+10s+8=0$

Answer to Problem 29E

The equation by completing square of $s^2+10s+8=0$ is $s=-5\pm \sqrt{17}$ .

Explanation of Solution

Given information:

  $s^2+10s+8=0$

The given equation is:

  $s^2+10s+8=0$

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

  $\begin{array}{l}a=1\\ b=10\\ c=8\end{array}$

Complete the Square ${\left(\frac{b}{2}\right)}^2$ to both the sides:

  ${\left(\frac{b}{2}\right)}^2={\left(\frac{10}{2}\right)}^2=25$

So,

  $s^2+10s+8+25=25$

Taking square root to both the sides:

  ${\left(s+5\right)}^2=\pm \sqrt{17}$

Simplify:

  $s+5=\pm \sqrt{17}$

Then:

  $s=-5\pm \sqrt{17}$