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Simplifying 11y2 + -248y + 576 = 0 Reorder the terms: 576 + -248y + 11y2 = 0 Solving 576 + -248y + 11y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 52.36363636 + -22.54545455y + y2 = 0 Move the constant term to the right: Add '-52.36363636' to each side of the equation. 52.36363636 + -22.54545455y + -52.36363636 + y2 = 0 + -52.36363636 Reorder the terms: 52.36363636 + -52.36363636 + -22.54545455y + y2 = 0 + -52.36363636 Combine like terms: 52.36363636 + -52.36363636 = 0.00000000 0.00000000 + -22.54545455y + y2 = 0 + -52.36363636 -22.54545455y + y2 = 0 + -52.36363636 Combine like terms: 0 + -52.36363636 = -52.36363636 -22.54545455y + y2 = -52.36363636 The y term is -22.54545455y. Take half its coefficient (-11.27272728). Square it (127.0743803) and add it to both sides. Add '127.0743803' to each side of the equation. -22.54545455y + 127.0743803 + y2 = -52.36363636 + 127.0743803 Reorder the terms: 127.0743803 + -22.54545455y + y2 = -52.36363636 + 127.0743803 Combine like terms: -52.36363636 + 127.0743803 = 74.71074394 127.0743803 + -22.54545455y + y2 = 74.71074394 Factor a perfect square on the left side: (y + -11.27272728)(y + -11.27272728) = 74.71074394 Calculate the square root of the right side: 8.643537698 Break this problem into two subproblems by setting (y + -11.27272728) equal to 8.643537698 and -8.643537698.Subproblem 1
y + -11.27272728 = 8.643537698 Simplifying y + -11.27272728 = 8.643537698 Reorder the terms: -11.27272728 + y = 8.643537698 Solving -11.27272728 + y = 8.643537698 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11.27272728' to each side of the equation. -11.27272728 + 11.27272728 + y = 8.643537698 + 11.27272728 Combine like terms: -11.27272728 + 11.27272728 = 0.00000000 0.00000000 + y = 8.643537698 + 11.27272728 y = 8.643537698 + 11.27272728 Combine like terms: 8.643537698 + 11.27272728 = 19.916264978 y = 19.916264978 Simplifying y = 19.916264978Subproblem 2
y + -11.27272728 = -8.643537698 Simplifying y + -11.27272728 = -8.643537698 Reorder the terms: -11.27272728 + y = -8.643537698 Solving -11.27272728 + y = -8.643537698 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11.27272728' to each side of the equation. -11.27272728 + 11.27272728 + y = -8.643537698 + 11.27272728 Combine like terms: -11.27272728 + 11.27272728 = 0.00000000 0.00000000 + y = -8.643537698 + 11.27272728 y = -8.643537698 + 11.27272728 Combine like terms: -8.643537698 + 11.27272728 = 2.629189582 y = 2.629189582 Simplifying y = 2.629189582Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.916264978, 2.629189582}
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