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algebra · worked example

Solve x² - 7x + 12 = 0 — x = 3 or x = 4

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

x2−7x+12=0x^2 - 7x + 12 = 0

Step-by-step solution

  1. 找出兩個數，使其相乘為 1212 且相加為 −7-7。

  2. 兩數皆須為負（乘積為正、和為負）：−3-3 與 −4-4 成立，因為 (−3)(−4)=12(-3)(-4) = 12 且 −3+(−4)=−7-3 + (-4) = -7。

  3. 因式分解：(x−3)(x−4)=0(x - 3)(x - 4) = 0。

  4. 令每個因式為零：x=3x = 3 或 x=4x = 4。

Answer

x=3orx=4x = 3 \quad \text{or} \quad x = 4

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