In this guide, we'll walk through Quadratic Equations — Complete Guide with Examples step by step. Whether you're revising for an exam or practising quadratic equations, this clear walkthrough will help you understand not just the answer, but the reasoning behind every step.

Quick Answer

See the step-by-step solution above for the complete answer.

Step-by-Step Solution

Step 1: Identify a=1, b=9, c=0

Step 2: Discriminant = 81

Step 3: Factor: (x + 9)(x - 0) = 0

Step 4: Identify a=1, b=9, c=0

Step 5: Discriminant = 81

Step 6: Factor: (x + 9)(x - 0) = 0

Step 7: Identify a=1, b=11, c=-12

Step 8: Discriminant = 169

Step 9: Factor: (x - 1)(x + 12) = 0

Step 10: Identify a=1, b=-6, c=9

Step 11: Discriminant = 0

Step 12: Factor: (x - 3)(x - 3) = 0

Step 13: Identify a=1, b=12, c=32

Step 14: Discriminant = 16

Step 15: Factor: (x + 4)(x + 8) = 0

Step 16: Identify a=1, b=6, c=-72

Step 17: Discriminant = 324

Step 18: Factor: (x - 6)(x + 12) = 0

Step 19: Identify a=1, b=-8, c=16

Step 20: Discriminant = 0

Step 21: Factor: (x - 4)(x - 4) = 0

Step 22: Identify a=1, b=11, c=0

Step 23: Discriminant = 121

Step 24: Factor: (x + 11)(x - 0) = 0

Step 25: Identify a=1, b=-1, c=-42

Step 26: Discriminant = 169

Step 27: Factor: (x + 6)(x - 7) = 0

Step 28: Identify a=1, b=0, c=-64

Step 29: Discriminant = 256

Step 30: Factor: (x - 8)(x + 8) = 0

Step 31: Identify a=1, b=23, c=132

Step 32: Discriminant = 1

Step 33: Factor: (x + 11)(x + 12) = 0

Step 34: Identify a=1, b=-7, c=0

Step 35: Discriminant = 49

Step 36: Factor: (x - 7)(x - 0) = 0

Step 37: Identify a=1, b=19, c=88

Step 38: Discriminant = 9

Step 39: Factor: (x + 11)(x + 8) = 0

Step 40: Identify a=1, b=-9, c=0

Step 41: Discriminant = 81

Step 42: Factor: (x - 9)(x - 0) = 0

Step 43: Identify a=1, b=5, c=-50

Step 44: Discriminant = 225

Step 45: Factor: (x - 5)(x + 10) = 0

Step 46: Identify a=1, b=13, c=40

Step 47: Discriminant = 9

Step 48: Factor: (x + 5)(x + 8) = 0

Step 49: Identify a=1, b=2, c=-24

Step 50: Discriminant = 100

Step 51: Factor: (x - 4)(x + 6) = 0

Step 52: Identify a=1, b=10, c=0

Step 53: Discriminant = 100

Step 54: Factor: (x + 10)(x - 0) = 0

Step 55: Identify a=1, b=-9, c=-10

Step 56: Discriminant = 121

Step 57: Factor: (x + 1)(x - 10) = 0

Step 58: Identify a=1, b=1, c=0

Step 59: Discriminant = 1

Step 60: Factor: (x - 0)(x + 1) = 0

Step 61: Identify a=1, b=-2, c=-99

Step 62: Discriminant = 400

Step 63: Factor: (x - 11)(x + 9) = 0

Why This Works

This problem uses quadratic equations. The key idea is to perform the same operation on both sides to keep the equation balanced. Each step brings you closer to isolating the unknown variable.

Common Mistakes to Avoid

❌ Mistake 1: Forgetting to apply the same operation to both sides of the equation.

❌ Mistake 2: Making sign errors when moving terms across the equals sign.

❌ Mistake 3: Not simplifying the final answer completely.

Practice Similar Problems

• Solve: x² + 9x + 0 = 0
• Solve: x² + 11x - 12 = 0
• Solve: x² - 6x + 9 = 0
• Solve: x² + 12x + 32 = 0
• Solve: x² + 6x - 72 = 0

Frequently Asked Questions