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algebra · worked example

Solve x² - 9 = 0 — x = 3 or x = -3

Method: difference of squares. Verified step-by-step solution with our free AI math solver.
Problem

x2−9=0x^2 - 9 = 0

Step-by-step solution

  1. Recognise x2−9x^2 - 9 as a difference of squares a2−b2a^2 - b^2 with a=xa = x and b=3b = 3.

  2. Apply the identity a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b): (x−3)(x+3)=0(x - 3)(x + 3) = 0.

  3. Set each factor to zero: x−3=0x - 3 = 0 or x+3=0x + 3 = 0.

  4. Solve: x=3x = 3 or x=−3x = -3.

Answer

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

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