\begin{tabular}{l|l} Use factoring to solve the equation. \\ \( c^{2}-2 c-35=0 \) & \( \begin{array}{l}\text { The solution is } c=\square \\ \text { (Type an integer or a simplified fraction. Use a comma to separate answers } \\ \text { as needed.) }\end{array} \)\end{tabular}

\[ \begin{array}{l} \text{The solution is } c = -5, \, 7 \\ \end{array} \] **Explanation:** To solve the quadratic equation \( c^{2} - 2c - 35 = 0 \) by factoring: 1. **Find two numbers that multiply to -35** (the constant term) **and add to -2** (the coefficient of the middle term). - The numbers are **5** and **-7** because: \[ 5 \times (-7) = -35 \quad \text{and} \quad 5 + (-7) = -2 \] 2. **Factor the quadratic equation** using these numbers: \[ c^{2} - 2c - 35 = (c + 5)(c - 7) = 0 \] 3. **Set each factor equal to zero** and solve for \( c \): \[ c + 5 = 0 \quad \Rightarrow \quad c = -5 \] \[ c - 7 = 0 \quad \Rightarrow \quad c = 7 \] So, the solutions are \( c = -5 \) and \( c = 7 \).