Solve x² − 5x + 6 = 0 Step by Step

Algebra 1GCSE

Problem

Solve the quadratic equation: x² − 5x + 6 = 0

📝Step-by-Step Solution

Identify the coefficients

Compare x² − 5x + 6 = 0 with the standard form ax² + bx + c = 0. We get: a = 1, b = −5, c = 6

a = 1, b = −5, c = 6

Calculate the discriminant

The discriminant Δ = b² − 4ac tells us how many solutions exist. Δ = (−5)² − 4(1)(6) = 25 − 24 = 1

Δ = (−5)² − 4(1)(6) = 1

Apply the quadratic formula

Substitute into x = (−b ± √Δ) / 2a. x = (−(−5) ± √1) / 2(1) = (5 ± 1) / 2

x = (5 ± 1) / 2

Calculate both solutions

Using +: x₁ = (5 + 1) / 2 = 6/2 = 3. Using −: x₂ = (5 − 1) / 2 = 4/2 = 2

x₁ = 3, x₂ = 2

✅Final Answer

x = 2 or x = 3

Both x = 2 and x = 3 are solutions. You can verify by substituting back: (2)² − 5(2) + 6 = 4 − 10 + 6 = 0 ✓ and (3)² − 5(3) + 6 = 9 − 15 + 6 = 0 ✓

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