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algebra · worked example

Solve x² + x - 6 = 0 — x = -3 or x = 2

Method: 因式分解. Verified step-by-step solution with our free AI math solver.
Problem

x2+x−6=0x^2 + x - 6 = 0

Step-by-step solution

  1. 找出兩個數，使其相乘為 −6-6 且相加為 11。

  2. 數對 (3,−2)(3, -2)：3⋅(−2)=−63 \cdot (-2) = -6 ✓，3+(−2)=13 + (-2) = 1 ✓。

  3. 因式分解：(x+3)(x−2)=0(x + 3)(x - 2) = 0。

  4. 令每個因式為零：x=−3x = -3 或 x=2x = 2。

Answer

x=−3orx=2x = -3 \quad \text{or} \quad x = 2

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