Solve for x in the equation x squared plus 11 x plus 121 fourths is equal to 125 fourths

The left side is a perfect square: x² + 11x + 121/4 = (x + 11/2)². So (x + 11/2)² = 125/4, and taking square roots gives x + 11/2 = ±√125/2 = ±5√5/2. Therefore x = −11/2 ± 5√5/2, which is choice A.

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