OG详解-OG6 数学1 Q18

Choice D is correct. Adding 40 to both sides of the given equation yields w² +12w = 40. To complete the square, adding 122​​ , or 6², to both sides of this equation yields w² +12w+62 = 40+6², or (w+6)² = 76. Taking the square root of both sides of this equation yields w+6 = ± √76​, or w+6 = ±2√19. Subtracting  6 from both sides of this equation yields w = -6±2√19​. Therefore, the solutions to the given equation are -6+2√19​ and -6-2√19​. Of these two solutions, only -6+2√19​ is given as a choice.
Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.