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algebra · worked example

Solve 5x² - 20 = 0 — x = 2 or x = -2

Method: 提取最大公因式 + 平方差. Verified step-by-step solution with our free AI math solver.
Problem

5x2−20=05x^2 - 20 = 0

Step-by-step solution

  1. 提取最大公因式 55：5(x2−4)=05(x^2 - 4) = 0。

  2. 辨識出平方差：x2−4=(x−2)(x+2)x^2 - 4 = (x-2)(x+2)。

  3. 完整因式分解：5(x−2)(x+2)=05(x - 2)(x + 2) = 0。

  4. 令二項式因式為零（常數 5 無法使乘積為零）：x=2x = 2 或 x=−2x = -2。

Answer

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

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