Chapter 9.5, Problem 30PPE

To determine

The solution of each equation by completing the square.

Answer to Problem 30PPE

  $v=7,-2$

Explanation of Solution

Given:

The given expression is:

  $2v^2-10v-20=8$

Calculation:

Calculate the value of v:

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

  $\begin{array}{l}2v^2-10v-20=8\\ 2v^2-10v=8+20\\ 2v^2-10v=28\\ \text{Divide both sides by 2:}\\ v^2-5v=14\\ \text{To make it a complete square, add }{\left(-\frac{5}{2}\right)}^2=\frac{25}{4}\text{ on both sides:}\\ v^2-5v+\frac{25}{4}=14+\frac{25}{4}\\ v^2-2\left(\frac{5}{2}\right)v+{\left(\frac{5}{2}\right)}^2=\frac{14}{1}·\frac{4}{4}+\frac{25}{4}·\frac{1}{1}\\ {\left(v-\frac{5}{2}\right)}^2=\frac{56+25}{4}\\ {\left(v-\frac{5}{2}\right)}^2=\frac{81}{4}\\ v-2.5=\pm \sqrt{20.25}\\ v-2.5=\pm 4.5\left(\text{Rounded to nearest hundredth}\right)\\ v-2.5=4.5\text{ or }v-2.5=-4.5\\ v=7\text{ or }v=-2\\ v=7,-2\end{array}$