Chapter 9.5, Problem 11P

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

$a^2-2a=15$

To determine

To solve : the equation by completing the square

Answer to Problem 11P

The solution of the equation is $a=5,-3$

Explanation of Solution

Given information :

The equation is

  $a^2-2a=15$

Calculation :

The solution of the equation is

  $\begin{array}{l}{a}^2-2a=15\\ a^2-2a+1=15+1\\ a^2-2\cdot a\cdot 1+{\left(1\right)}^2=16\\ {\left(a-1\right)}^2=16\\ \left(a-1\right)=\pm \sqrt{16}\\ a-1=\pm 4\\ a=1\pm 4\\ a=5,-3\end{array}$

Hence, the solution of the equation is $a=5,-3$ .