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Complete the square

x^2 - 2x - 14 = 0

1 Answer

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To complete the square for the equation x^2 - 2x - 14 = 0, follow these steps:

1. Move the constant term to the right side of the equation: x^2 - 2x = 14

2. Take half of the coefficient of x, square it, and add it to both sides of the equation: x^2 - 2x + 1 = 15

3. Factor the left side of the equation as a perfect square: (x - 1)^2 = 15

4. Take the square root of both sides of the equation, remembering to include both the positive and negative square roots: x - 1 = ±√15

5. Add 1 to both sides of the equation to isolate x: x = 1 ± √15

Therefore, the solutions to the equation x^2 - 2x - 14 = 0 are x = 1 + √15 and x = 1 - √15.
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