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algebra · worked example

Solve x² + 7x + 10 = 0 — x = -2 or x = -5

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

x2+7x+10=0x^2 + 7x + 10 = 0

Step-by-step solution

  1. 找出兩個相乘為 1010、相加為 77 的數。

  2. 配對 (2,5)(2, 5)：2⋅5=102 \cdot 5 = 10 ✓，2+5=72 + 5 = 7 ✓。

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

  4. 求解：x=−2x = -2 或 x=−5x = -5。

Answer

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

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