To determine which equations have both \(-6\) and \(6\) as possible values for \(c\), we can solve each equation one by one.
Choice A: \[c^2 = 36.\]
To solve for \(c\): Taking the square root of both sides gives: \[c = \sqrt{36} \quad \text{or} \quad c = -\sqrt{36}.\] This results in: \[c = 6 \quad \text{or} \quad c = -6.\] Thus, both values \(-6\) and \(6\) are solutions. This choice is valid.
Choice B: \[c^3 = 216.\]
To solve for \(c\): Taking the cube root of both sides gives: \[c = \sqrt[3]{216}.\] Calculating the cube root: \[c = 6.\] Since the cube root has only one real solution, \(-6\) is not a solution. This choice is not valid.
Choice C: States "None of the above." Since we found a valid equation in Choice A, this choice is also not applicable.
The final result shows that the only valid equation that has both \(-6\) and \(6\) as possible values of \(c\) is:
Choice A: \(c^2 = 36\)