Chapter 12.4, Problem 3ST

To determine

To solve: the given equation for $a$ by completing square method.

Answer to Problem 3ST

  $a=7,5$

Explanation of Solution

Given:

Given equation

  $a^2-12a+35=0$

Concept used:

A perfect square trinomial is of the form $a^2+2ab+b^2$ and the perfect square will be

  $a^2+2ab+b^2={\left(a+b\right)}^2$

Calculation:

Consider the given equation,

  $a^2-12a+35=0$

Make the left side a perfect square of the above equation by completing square method as shown:

  $\begin{array}{c}{a}^2-12a+36=1\\ a^2-2\cdot a\cdot 6+6^2=1^2\\ {\left(a-6\right)}^2=1\end{array}$

The equation can be solved by square root as:

  $\begin{array}{c}{\left(a-6\right)}^2=1\\ a-6=\pm \sqrt{1}\\ a=\pm 1+6\\ a=7,5\end{array}$

Hence, the solution is $a=7,5$ .