X²-10x-11=0 x²-9x-10=0 x²+8x-9=0 x²+9x+20=0 x²-15x+36=0 x²+5x-14=0 x²-7x-30=0

To solve each of these quadratic equations, we can either apply the quadratic formula or factor them when possible. Let's go through each equation one by one. 1. **Equation**: \( x^2 - 10x - 11 = 0 \) - Using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \): - Here, \( a = 1, b = -10, c = -11 \) - \( b^2 - 4ac = 100 + 44 = 144 \) - \( x = \frac{10 \pm 12}{2} \) - Solutions: \( x = 11 \) and \( x = -1 \) 2. **Equation**: \( x^2 - 9x - 10 = 0 \) - Factorable form: \( (x - 10)(x + 1) = 0 \) - Solutions: \( x = 10 \) and \( x = -1 \) 3. **Equation**: \( x^2 + 8x - 9 = 0 \) - Using the quadratic formula: - Here, \( a = 1, b = 8, c = -9 \) - \( b^2 - 4ac = 64 + 36 = 100 \) - \( x = \frac{-8 \pm 10}{2} \) - Solutions: \( x = 1 \) and \( x = -9 \) 4. **Equation**: \( x^2 + 9x + 20 = 0 \) - Factorable form: \( (x + 5)(x + 4) = 0 \) - Solutions: \( x = -5 \) and \( x = -4 \) 5. **Equation**: \( x^2 - 15x + 36 = 0 \) - Factorable form: \( (x - 12)(x - 3) = 0 \) - Solutions: \( x = 12 \) and \( x = 3 \) 6. **Equation**: \( x^2 + 5x - 14 = 0 \) - Using the quadratic formula: - Here, \( a = 1, b = 5, c = -14 \) - \( b^2 - 4ac = 25 + 56 = 81 \) - \( x = \frac{-5 \pm 9}{2} \) - Solutions: \( x = 2 \) and \( x = -7 \) 7. **Equation**: \( x^2 - 7x - 30 = 0 \) - Factorable form: \( (x - 10)(x + 3) = 0 \) - Solutions: \( x = 10 \) and \( x = -3 \) ### Summary of Solutions: 1. \( x^2 - 10x - 11 = 0 \) → \( x = 11, -1 \) 2. \( x^2 - 9x - 10 = 0 \) → \( x = 10, -1 \) 3. \( x^2 + 8x - 9 = 0 \) → \( x = 1, -9 \) 4. \( x^2 + 9x + 20 = 0 \) → \( x = -5, -4 \) 5. \( x^2 - 15x + 36 = 0 \) → \( x = 12, 3 \) 6. \( x^2 + 5x - 14 = 0 \) → \( x = 2, -7 \) 7. \( x^2 - 7x - 30 = 0 \) → \( x = 10, -3 \)