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Simplifying 11y2 + 19y + -60 = 0 Reorder the terms: -60 + 19y + 11y2 = 0 Solving -60 + 19y + 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'. -5.454545455 + 1.727272727y + y2 = 0 Move the constant term to the right: Add '5.454545455' to each side of the equation. -5.454545455 + 1.727272727y + 5.454545455 + y2 = 0 + 5.454545455 Reorder the terms: -5.454545455 + 5.454545455 + 1.727272727y + y2 = 0 + 5.454545455 Combine like terms: -5.454545455 + 5.454545455 = 0.000000000 0.000000000 + 1.727272727y + y2 = 0 + 5.454545455 1.727272727y + y2 = 0 + 5.454545455 Combine like terms: 0 + 5.454545455 = 5.454545455 1.727272727y + y2 = 5.454545455 The y term is 1.727272727y. Take half its coefficient (0.8636363635). Square it (0.7458677684) and add it to both sides. Add '0.7458677684' to each side of the equation. 1.727272727y + 0.7458677684 + y2 = 5.454545455 + 0.7458677684 Reorder the terms: 0.7458677684 + 1.727272727y + y2 = 5.454545455 + 0.7458677684 Combine like terms: 5.454545455 + 0.7458677684 = 6.2004132234 0.7458677684 + 1.727272727y + y2 = 6.2004132234 Factor a perfect square on the left side: (y + 0.8636363635)(y + 0.8636363635) = 6.2004132234 Calculate the square root of the right side: 2.490062895 Break this problem into two subproblems by setting (y + 0.8636363635) equal to 2.490062895 and -2.490062895.Subproblem 1
y + 0.8636363635 = 2.490062895 Simplifying y + 0.8636363635 = 2.490062895 Reorder the terms: 0.8636363635 + y = 2.490062895 Solving 0.8636363635 + y = 2.490062895 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.8636363635' to each side of the equation. 0.8636363635 + -0.8636363635 + y = 2.490062895 + -0.8636363635 Combine like terms: 0.8636363635 + -0.8636363635 = 0.0000000000 0.0000000000 + y = 2.490062895 + -0.8636363635 y = 2.490062895 + -0.8636363635 Combine like terms: 2.490062895 + -0.8636363635 = 1.6264265315 y = 1.6264265315 Simplifying y = 1.6264265315Subproblem 2
y + 0.8636363635 = -2.490062895 Simplifying y + 0.8636363635 = -2.490062895 Reorder the terms: 0.8636363635 + y = -2.490062895 Solving 0.8636363635 + y = -2.490062895 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.8636363635' to each side of the equation. 0.8636363635 + -0.8636363635 + y = -2.490062895 + -0.8636363635 Combine like terms: 0.8636363635 + -0.8636363635 = 0.0000000000 0.0000000000 + y = -2.490062895 + -0.8636363635 y = -2.490062895 + -0.8636363635 Combine like terms: -2.490062895 + -0.8636363635 = -3.3536992585 y = -3.3536992585 Simplifying y = -3.3536992585Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.6264265315, -3.3536992585}
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