Question

convert the equation into vertex form, then solve the equation: r^2– 4r – 91 = 7

Answer 1

We want to convert the equation to vertex form

$\begin{gathered} r^2-4r-91=7 \\ r^2-4r\text{ = 98} \\ r^2-4r\text{ + }(-2)^2=98+(-2)^2 \\ (r-2)^2=102\text{ },(r-2)^2-102=0,\text{ This is the equation in vertex form} \\ r-2\text{ =}\pm\sqrt[]{102} \\ r\text{ = 2}\pm\sqrt[]{102} \\ \end{gathered}$$\begin{gathered} \text{Equation in vertex form, (r-2)}^2-102\text{ = 0} \\ \text{Solution, r = 2}\pm\sqrt[]{102} \end{gathered}$