Chapter 9.5, Problem 12P

Solve each equation by completing the square. If necessary, round to the nearest hundredth.

$v^2+8v=15$

To determine

To solve : the equation by completing the square

Answer to Problem 12P

The solution of the equation is $v=-1.6,-9.6$

Explanation of Solution

Given information :

The equation is

  $v^2+8v=15$

Calculation :

The solution of the equation is

  $\begin{array}{l}{v}^2+8v=15\\ v^2+8v+16=15+16\\ v^2+2\cdot v\cdot 4+{\left(4\right)}^2=31\\ {\left(v+4\right)}^2=31\\ \left(v+4\right)=\pm \sqrt{31}\\ v+4=\pm 5.57\\ v=-4\pm 5.57\\ v=-1.6,-9.6\end{array}$

Hence, the solution of the equation is $v=-1.6,-9.6$ .