Chapter 9.5, Problem 13P

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

$y^2+16y=17$

To determine

To solve : the equation by completing the square

Answer to Problem 13P

The solution of the equation is $y=1,-17$

Explanation of Solution

Given information :

The equation is

  $y^2+16y=17$

Calculation :

The solution of the equation is

  $\begin{array}{l}{y}^2+16y=17\\ y^2+16y+64=17+64\\ y^2+2\cdot y\cdot 8+{\left(8\right)}^2=81\\ {\left(y+8\right)}^2=81\\ \left(y+8\right)=\pm \sqrt{81}\\ y+8=\pm 9\\ y=-8\pm 9\\ y=1,-17\end{array}$

Hence, the solution of the equation is $y=1,-17$ .