9) \( r^{2}-4 r-91=7 \)

Let's start by simplifying the equation. First, move 7 to the left side: \( r^{2} - 4r - 91 - 7 = 0 \) This simplifies to: \( r^{2} - 4r - 98 = 0 \) Now, we can factor this quadratic equation. We look for two numbers that multiply to -98 and add to -4. These numbers are -14 and 7. Thus, we can factor it as: \( (r - 14)(r + 7) = 0 \) Setting each factor equal to zero gives us the solutions: 1. \( r - 14 = 0 \) → \( r = 14 \) 2. \( r + 7 = 0 \) → \( r = -7 \) So the solutions to the equation \( r^{2} - 4r - 91 = 7 \) are \( r = 14 \) and \( r = -7 \). Now let's summarize these solutions: \( r = 14 \) or \( r = -7 \).