Problem
Solve using the quadratic formula: x² + 2x - 8 = 0
📝Step-by-Step Solution
1
Write the quadratic formula
The quadratic formula solves any equation of the form ax² + bx + c = 0
x = (-b ± √(b² - 4ac)) / 2a
2
Identify a, b, and c
From x² + 2x - 8 = 0: a = 1 (coefficient of x²), b = 2 (coefficient of x), c = -8 (constant)
a = 1, b = 2, c = -8
3
Calculate the discriminant
Find b² - 4ac: (2)² - 4(1)(-8) = 4 + 32 = 36
b² - 4ac = 4 + 32 = 36
4
Substitute into the formula
x = (-2 ± √36) / 2(1) = (-2 ± 6) / 2
x = (-2 ± 6) / 2
5
Find both solutions
x₁ = (-2 + 6) / 2 = 4/2 = 2. x₂ = (-2 - 6) / 2 = -8/2 = -4
x₁ = 2, x₂ = -4
✅Final Answer
x = 2 or x = -4
The discriminant (36) is positive and a perfect square, giving us two rational solutions. Check: (2)² + 2(2) - 8 = 4 + 4 - 8 = 0 ✓ and (-4)² + 2(-4) - 8 = 16 - 8 - 8 = 0 ✓
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