Use factoring to solve the quadratic equation. Check by \( x^{2}-5 x-14=0 \) Rewrite the equation in factored form. \( (x-7)(x+2)=0 \) (Factor completely.) The solution set is \( \{\square\} \) (Use a comma to separate answers as needed. Type

To solve the quadratic equation \( x^{2} - 5x - 14 = 0 \) by factoring, follow these steps: 1. **Factor the quadratic:** The equation factors to: \[ (x - 7)(x + 2) = 0 \] 2. **Set each factor equal to zero and solve for \( x \):** \[ x - 7 = 0 \quad \Rightarrow \quad x = 7 \] \[ x + 2 = 0 \quad \Rightarrow \quad x = -2 \] 3. **Write the solution set:** \[ \{7, -2\} \] **Verification:** Plugging the solutions back into the original equation to verify: - For \( x = 7 \): \[ (7)^2 - 5(7) - 14 = 49 - 35 - 14 = 0 \] - For \( x = -2 \): \[ (-2)^2 - 5(-2) - 14 = 4 + 10 - 14 = 0 \] Both solutions satisfy the original equation. **Final Answer:** \(\{7, -2\}\)