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algebra · worked example

Solve 2x² - 3x - 2 = 0

Method: สูตรกำลังสอง. Verified step-by-step solution with our free AI math solver.
Problem

2x2−3x−2=02x^2 - 3x - 2 = 0

Step-by-step solution

  1. ระบุ a=2a = 2, b=−3b = -3, c=−2c = -2

  2. คำนวณดิสคริมิแนนต์: Δ=(−3)2−4(2)(−2)=9+16=25\Delta = (-3)^2 - 4(2)(-2) = 9 + 16 = 25

  3. ใช้สูตรกำลังสอง: x=3±252⋅2=3±54x = \frac{3 \pm \sqrt{25}}{2 \cdot 2} = \frac{3 \pm 5}{4}

  4. ได้สองคำตอบ: x1=3+54=2x_1 = \frac{3 + 5}{4} = 2 และ x2=3−54=−12x_2 = \frac{3 - 5}{4} = -\frac{1}{2}

Answer

x=2orx=−12x = 2 \quad \text{or} \quad x = -\tfrac{1}{2}

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