w 2 + 12 w - 40 = 0 Which of the following is a solution to the given equation?

Question

Accepted Answer

Choice D is correct. Adding 40 to both sides of the given equation yields w 2 + 12 w = 40 . To complete the square, adding 12 2 2 , or 6 2 , to both sides of this equation yields w 2 + 12 w + 6 2 = 40 + 6 2 , or w + 6 2 = 76 . Taking the square root of both sides of this equation yields w + 6 = &#177; 76 , or w + 6 = &#177; 2 19 . Subtracting 6 from both sides of this equation yields w = - 6 &#177; 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.

Question w-2-12