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algebra · worked example

Solve x² + 3x - 10 = 0 — x = -5 or x = 2

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

x2+3x−10=0x^2 + 3x - 10 = 0

Step-by-step solution

  1. 找出兩個相乘為 −10-10、相加為 33 的數。

  2. 配對 (5,−2)(5, -2)：5⋅(−2)=−105 \cdot (-2) = -10 ✓，5+(−2)=35 + (-2) = 3 ✓。

  3. 因式分解：(x+5)(x−2)=0(x + 5)(x - 2) = 0。

  4. 令每個因式為零：x=−5x = -5 或 x=2x = 2。

Answer

x=−5orx=2x = -5 \quad \text{or} \quad x = 2

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