Medium📚 Quadratic Formula

Quadratic Formula Example

Algebra 1GCSEÅrskurs 9

Problem

Solve using the quadratic formula: x² + 2x - 8 = 0

📝Step-by-Step Solution

Write the quadratic formula

The quadratic formula solves any equation of the form ax² + bx + c = 0

x = (-b ± √(b² - 4ac)) / 2a

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

Calculate the discriminant

Find b² - 4ac: (2)² - 4(1)(-8) = 4 + 32 = 36

b² - 4ac = 4 + 32 = 36

Substitute into the formula

x = (-2 ± √36) / 2(1) = (-2 ± 6) / 2

x = (-2 ± 6) / 2

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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