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algebra · worked example

Solve x² + x - 6 = 0 — x = -3 or x = 2

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

x2+x−6=0x^2 + x - 6 = 0

Step-by-step solution

  1. Find two numbers multiplying to −6-6 and adding to 11.

  2. Pair (3,−2)(3, -2): 3⋅(−2)=−63 \cdot (-2) = -6 ✓, 3+(−2)=13 + (-2) = 1 ✓.

  3. Factor: (x+3)(x−2)=0(x + 3)(x - 2) = 0.

  4. Set each factor to zero: x=−3x = -3 or x=2x = 2.

Answer

x=−3orx=2x = -3 \quad \text{or} \quad x = 2

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