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Solve for x over the real numbers:
2 x^2 - 4 x - 3 = 0

Divide both sides by 2:
x^2 - 2 x - 3/2 = 0

Add 3/2 to both sides:
x^2 - 2 x = 3/2

Add 1 to both sides:
x^2 - 2 x + 1 = 5/2

Write the left hand side as a square:
(x - 1)^2 = 5/2

Take the square root of both sides:
x - 1 = sqrt(5/2) or x - 1 = -sqrt(5/2)

Add 1 to both sides:
x = 1 + sqrt(5/2) or x - 1 = -sqrt(5/2)

Add 1 to both sides:
Answer: x = 1 + sqrt(5/2) or x = 1 - sqrt(5/2)

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