Question

Solve the quadratic equation using square root property.

$6c^2+4=29$

Short answer

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

Step-by-step solution

Given Information.    

The Given equation is$6c^2+4=29$.

Isolate the binomial term.  

$$\begin{gathered} 6c^2=29-46 \\ {c}^2=25 \\ {c}^2=\frac{25}{6} \end{gathered}$$

Use the Square Root Property.   

$c=\pm \sqrt{\frac{25}{6}}$

Factor the radical.

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

Rationalize the denominator.

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

Rewrite to show two solutions.

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