Question

Solve by completing the square :

$3r^2-2r=21$

Short answer

The required value of$r$is$3,\frac{-7}{3}$

Step-by-step solution

Given information

$3r^2-2r=21$

Calculation

$$\begin{gathered} 3r^2-2r=21 \\ \Rightarrow \frac{3r^2-2r}{3}=\frac{21}{3}+\frac{1}{9} \\ \Rightarrow r^2-\frac{2}{3}r=7 \\ \Rightarrow r^2-\frac{2}{3}r+(\frac{1}{2}\times {(-\frac{2}{3}))}^2=7 \\ \Rightarrow r^2-\frac{2}{3}r+\frac{1}{9}=7+\frac{1}{9} \\ \Rightarrow {(r-\frac{1}{3})}^2=\frac{64}{9} \\ \Rightarrow r-\frac{1}{3}=\pm \sqrt{\frac{64}{9}} \\ \Rightarrow r=\frac{1}{3}\pm \sqrt{\frac{64}{9}} \\ =\frac{1}{3}\pm \frac{8}{3} \\ =\frac{1+8}{3},\frac{1-8}{3} \\ =\frac{9}{3},\frac{-7}{3} \\ =3,\frac{-7}{3} \end{gathered}$$

The required value of$r$is$3,\frac{-7}{3}$