Chapter 9.5, Problem 25PPE

To determine

The solution of each equation by completing the square.

Answer to Problem 25PPE

  $a=-1.65,3.65$

Explanation of Solution

Given:

The given expression is:

  $4a^2-8a=24$

Calculation:

Calculate the value of a:

Change the given equation in the form $m^2=n$ and then solve it further.

  $\begin{array}{l}4a^2-8a=24\\ \text{Divide both sides by 4:}\\ a^2-2a=6\\ \text{To make it a complete square, add }{\left(\frac{2}{2}\right)}^2=1\text{ on both sides:}\\ a^2-2a+1=6+1\\ a^2-2\left(1\right)\left(a\right)+1^2=7\\ {\left(a-1\right)}^2=7\\ a-1=\pm \sqrt{7}\\ a-1=\pm 2.65\\ a-1=2.65\text{ or }a-1=-2.65\\ a=3.65\text{ or }a=-1.65\\ a=-1.65,3.65\end{array}$