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Simplifying 12y2 + 47y + -14 = 0 Reorder the terms: -14 + 47y + 12y2 = 0 Solving -14 + 47y + 12y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.166666667 + 3.916666667y + y2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + 3.916666667y + 1.166666667 + y2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + 3.916666667y + y2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + 3.916666667y + y2 = 0 + 1.166666667 3.916666667y + y2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 3.916666667y + y2 = 1.166666667 The y term is 3.916666667y. Take half its coefficient (1.958333334). Square it (3.835069447) and add it to both sides. Add '3.835069447' to each side of the equation. 3.916666667y + 3.835069447 + y2 = 1.166666667 + 3.835069447 Reorder the terms: 3.835069447 + 3.916666667y + y2 = 1.166666667 + 3.835069447 Combine like terms: 1.166666667 + 3.835069447 = 5.001736114 3.835069447 + 3.916666667y + y2 = 5.001736114 Factor a perfect square on the left side: (y + 1.958333334)(y + 1.958333334) = 5.001736114 Calculate the square root of the right side: 2.236456151 Break this problem into two subproblems by setting (y + 1.958333334) equal to 2.236456151 and -2.236456151.Subproblem 1
y + 1.958333334 = 2.236456151 Simplifying y + 1.958333334 = 2.236456151 Reorder the terms: 1.958333334 + y = 2.236456151 Solving 1.958333334 + y = 2.236456151 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.958333334' to each side of the equation. 1.958333334 + -1.958333334 + y = 2.236456151 + -1.958333334 Combine like terms: 1.958333334 + -1.958333334 = 0.000000000 0.000000000 + y = 2.236456151 + -1.958333334 y = 2.236456151 + -1.958333334 Combine like terms: 2.236456151 + -1.958333334 = 0.278122817 y = 0.278122817 Simplifying y = 0.278122817Subproblem 2
y + 1.958333334 = -2.236456151 Simplifying y + 1.958333334 = -2.236456151 Reorder the terms: 1.958333334 + y = -2.236456151 Solving 1.958333334 + y = -2.236456151 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.958333334' to each side of the equation. 1.958333334 + -1.958333334 + y = -2.236456151 + -1.958333334 Combine like terms: 1.958333334 + -1.958333334 = 0.000000000 0.000000000 + y = -2.236456151 + -1.958333334 y = -2.236456151 + -1.958333334 Combine like terms: -2.236456151 + -1.958333334 = -4.194789485 y = -4.194789485 Simplifying y = -4.194789485Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.278122817, -4.194789485}
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