Quadratic Equation Practice
Master quadratic equations with problems covering all solution methods. Learn when to factor, when to use the quadratic formula, and how to complete the square.
Skills You'll Practice
- Solving by factoring
- Using the quadratic formula
- Completing the square
- Finding the discriminant
- Solving quadratic word problems
- Understanding the nature of roots
Solving by Factoring
Easyx² - 9 = 0
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Difference of squares: (x+3)(x-3) = 0
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x = 3 or x = -3
x² + 5x = 0
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Factor out x: x(x+5) = 0
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x = 0 or x = -5
x² + 5x + 6 = 0
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Find two numbers that multiply to 6 and add to 5
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x = -2 or x = -3
Quadratic Formula
Mediumx² + 2x - 8 = 0 (use the formula)
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a=1, b=2, c=-8. Discriminant = 4+32 = 36
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x = 2 or x = -4
2x² - 5x - 3 = 0
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a=2, b=-5, c=-3
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x = 3 or x = -1/2
x² - 4x + 1 = 0
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Discriminant = 16-4 = 12
✓ Show Answer
x = 2 ± √3
Completing the Square
HardSolve by completing the square: x² + 6x + 5 = 0
💡 Show Hint
x² + 6x + 9 = -5 + 9 → (x+3)² = 4
✓ Show Answer
x = -1 or x = -5
Solve: x² - 8x + 7 = 0 by completing the square
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(x-4)² = 16 - 7 = 9
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x = 7 or x = 1
How many real solutions? x² + 4x + 5 = 0
💡 Show Hint
Check b² - 4ac = 16 - 20
✓ Show Answer
No real solutions (discriminant = -4)
Pro Tips
- 💡Try factoring first—it's usually the fastest method when it works
- 💡The quadratic formula ALWAYS works: x = (-b ± √(b²-4ac)) / 2a
- 💡If discriminant > 0: two real solutions. = 0: one solution. < 0: no real solutions
- 💡Completing the square is useful for finding vertex form and deriving the formula
Curriculum Alignment
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