Question

Solve$5r^2-2=34$

Short answer

The solutions are$r=\pm \frac{6\sqrt{5}}{5}$.

Step-by-step solution

Given Information.  

The Given equation is$5r^2-2=34$.

Isolate the quadratic term and makes its coefficient one.   

$$\begin{gathered} 5r^2=34+25 \\ {r}^2=36 \end{gathered}$$

 Use the square root property.  

$$\begin{gathered} r^2=\frac{36}{5} \\ r=\pm \sqrt{\frac{36}{5}} \end{gathered}$$

Factor the radical.

$$\begin{gathered} r=\pm \sqrt{\frac{36}{5}} \\ r=\pm \sqrt{\frac{6\times 6}{5}} \\ r=\pm \frac{6}{\sqrt{5}} \end{gathered}$$

Rationalize the denominator.

$$\begin{gathered} r=\pm \frac{6}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}} \\ r=\pm \frac{6\sqrt{5}}{5} \end{gathered}$$

Rewrite to show two solutions.

$$\begin{gathered} r=\frac{6\sqrt{5}}{5}, \\ r=-\frac{6\sqrt{5}}{5} \end{gathered}$$