Chapter 9.5, Problem 8P

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

$p^2-5p=-4$

To determine

To solve : the equation by completing the square

Answer to Problem 8P

The solution of the equation is $z=4,1$

Explanation of Solution

Given information :

The equation is

  $p^2-5p=-4$

Calculation :

The solution of the equation is

  $\begin{array}{l}{p}^2-5p=-4\\ p^2-5p+\frac{25}{4}=-4+\frac{25}{4}\\ p^2-2\cdot p\cdot \frac{5}{2}+{\left(\frac{5}{2}\right)}^2=\frac{-16+25}{4}\\ {\left(p-\frac{5}{2}\right)}^2=\frac{9}{4}\\ \left(p-\frac{5}{2}\right)=\pm \sqrt{\frac{9}{4}}\\ p-\frac{5}{2}=\pm \frac{3}{2}\\ p=\frac{5}{2}\pm \frac{3}{2}\\ p=4,1\end{array}$

Hence, the solution of the equation is $z=4,1$ .