Chapter 9 - Quadratic Functions and Equations - 9-5 Completing the Square - Practice and Problem-Solving Exercises - Page 579: 14

$r=7.83,-3.83$

$r^2-4r=30$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-4$ Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-4)^2}{4}=4$ To complete the square, add $4$ on both sides. $r^2-4r+4=30+4$ $\implies (r-2)^2=34$ $\implies r-2=5.8$ and $\implies r-2=-5.8$ or, $r=7.8,-3.8$