Question Use the square roots property to solve the quadratic equation \( c^{2}+12 c+36=121 \). If there are multiple answers, list them separated by a comma, e.g. 1, 2. If there is no solution, enter \( \varnothing \). Provide your answer below:

To solve the equation \( c^{2}+12 c+36=121 \), we first simplify it: 1. Move 121 to the left side: \( c^{2}+12 c+36-121=0 \) becomes \( c^{2}+12 c-85=0 \). Next, we can factor or use the square root property. The left side is a perfect square trinomial, so we have: 2. \( (c+6)^{2}=85 \) 3. Taking the square root of both sides gives us two potential solutions: \( c+6 = \sqrt{85} \) and \( c+6 = -\sqrt{85} \). 4. Solving for \( c \) results in: \( c = -6 + \sqrt{85} \) and \( c = -6 - \sqrt{85} \). Finally, the solutions are: \[ c = -6 + \sqrt{85}, -6 - \sqrt{85} \]