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Simplifying 11y(y + -2) + 3y = -7y + 14 Reorder the terms: 11y(-2 + y) + 3y = -7y + 14 (-2 * 11y + y * 11y) + 3y = -7y + 14 (-22y + 11y2) + 3y = -7y + 14 Reorder the terms: -22y + 3y + 11y2 = -7y + 14 Combine like terms: -22y + 3y = -19y -19y + 11y2 = -7y + 14 Reorder the terms: -19y + 11y2 = 14 + -7y Solving -19y + 11y2 = 14 + -7y Solving for variable 'y'. Reorder the terms: -14 + -19y + 7y + 11y2 = 14 + -7y + -14 + 7y Combine like terms: -19y + 7y = -12y -14 + -12y + 11y2 = 14 + -7y + -14 + 7y Reorder the terms: -14 + -12y + 11y2 = 14 + -14 + -7y + 7y Combine like terms: 14 + -14 = 0 -14 + -12y + 11y2 = 0 + -7y + 7y -14 + -12y + 11y2 = -7y + 7y Combine like terms: -7y + 7y = 0 -14 + -12y + 11y2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.272727273 + -1.090909091y + y2 = 0 Move the constant term to the right: Add '1.272727273' to each side of the equation. -1.272727273 + -1.090909091y + 1.272727273 + y2 = 0 + 1.272727273 Reorder the terms: -1.272727273 + 1.272727273 + -1.090909091y + y2 = 0 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + -1.090909091y + y2 = 0 + 1.272727273 -1.090909091y + y2 = 0 + 1.272727273 Combine like terms: 0 + 1.272727273 = 1.272727273 -1.090909091y + y2 = 1.272727273 The y term is -1.090909091y. Take half its coefficient (-0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. -1.090909091y + 0.2975206612 + y2 = 1.272727273 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091y + y2 = 1.272727273 + 0.2975206612 Combine like terms: 1.272727273 + 0.2975206612 = 1.5702479342 0.2975206612 + -1.090909091y + y2 = 1.5702479342 Factor a perfect square on the left side: (y + -0.5454545455)(y + -0.5454545455) = 1.5702479342 Calculate the square root of the right side: 1.253095341 Break this problem into two subproblems by setting (y + -0.5454545455) equal to 1.253095341 and -1.253095341.Subproblem 1
y + -0.5454545455 = 1.253095341 Simplifying y + -0.5454545455 = 1.253095341 Reorder the terms: -0.5454545455 + y = 1.253095341 Solving -0.5454545455 + y = 1.253095341 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + y = 1.253095341 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + y = 1.253095341 + 0.5454545455 y = 1.253095341 + 0.5454545455 Combine like terms: 1.253095341 + 0.5454545455 = 1.7985498865 y = 1.7985498865 Simplifying y = 1.7985498865Subproblem 2
y + -0.5454545455 = -1.253095341 Simplifying y + -0.5454545455 = -1.253095341 Reorder the terms: -0.5454545455 + y = -1.253095341 Solving -0.5454545455 + y = -1.253095341 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + y = -1.253095341 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + y = -1.253095341 + 0.5454545455 y = -1.253095341 + 0.5454545455 Combine like terms: -1.253095341 + 0.5454545455 = -0.7076407955 y = -0.7076407955 Simplifying y = -0.7076407955Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.7985498865, -0.7076407955}
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