Chapter 9.5, Problem 16PPE

To determine

The solution of given equation by completing the square.

Answer to Problem 16PPE

  $a=-5,7$

Explanation of Solution

Given:

The given expression is:

  $a^2-2a-35=0$

Calculation:

The expression $x^2+bx$ becomes a perfect trinomial by adding ${\left(\frac{b}{2}\right)}^2\text{ to }{x}^2+bx.$

Convert the given equation in the form $x^2+bx$ :

  $a^2-2a=35$

In given expression, the value of b is -2.

Therefore,

  $\begin{array}{l}\text{Add }{\left(\frac{-2}{2}\right)}^2\text{to both sides for equation to become complete square}\text{.}\\ a^2-2a+1=35+1\\ {\left(a-1\right)}^2=36\\ a-1=\pm \sqrt{36}\\ a-1=\pm 6\\ a-1=6\text{ or }a-1=-6\\ a=7\text{ or }a=-5\\ a=-5,7\end{array}$