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Simplifying 0.16y(y + -3) + 0.12 = 0.08y + -0.1 Reorder the terms: 0.16y(-3 + y) + 0.12 = 0.08y + -0.1 (-3 * 0.16y + y * 0.16y) + 0.12 = 0.08y + -0.1 (-0.48y + 0.16y2) + 0.12 = 0.08y + -0.1 Reorder the terms: 0.12 + -0.48y + 0.16y2 = 0.08y + -0.1 Reorder the terms: 0.12 + -0.48y + 0.16y2 = -0.1 + 0.08y Solving 0.12 + -0.48y + 0.16y2 = -0.1 + 0.08y Solving for variable 'y'. Reorder the terms: 0.12 + 0.1 + -0.48y + -0.08y + 0.16y2 = -0.1 + 0.08y + 0.1 + -0.08y Combine like terms: 0.12 + 0.1 = 0.22 0.22 + -0.48y + -0.08y + 0.16y2 = -0.1 + 0.08y + 0.1 + -0.08y Combine like terms: -0.48y + -0.08y = -0.56y 0.22 + -0.56y + 0.16y2 = -0.1 + 0.08y + 0.1 + -0.08y Reorder the terms: 0.22 + -0.56y + 0.16y2 = -0.1 + 0.1 + 0.08y + -0.08y Combine like terms: -0.1 + 0.1 = 0.0 0.22 + -0.56y + 0.16y2 = 0.0 + 0.08y + -0.08y 0.22 + -0.56y + 0.16y2 = 0.08y + -0.08y Combine like terms: 0.08y + -0.08y = 0.00 0.22 + -0.56y + 0.16y2 = 0.00 Begin completing the square. Divide all terms by 0.16 the coefficient of the squared term: Divide each side by '0.16'. 1.375 + -3.5y + y2 = 0 Move the constant term to the right: Add '-1.375' to each side of the equation. 1.375 + -3.5y + -1.375 + y2 = 0 + -1.375 Reorder the terms: 1.375 + -1.375 + -3.5y + y2 = 0 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + -3.5y + y2 = 0 + -1.375 -3.5y + y2 = 0 + -1.375 Combine like terms: 0 + -1.375 = -1.375 -3.5y + y2 = -1.375 The y term is -3.5y. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5y + 3.0625 + y2 = -1.375 + 3.0625 Reorder the terms: 3.0625 + -3.5y + y2 = -1.375 + 3.0625 Combine like terms: -1.375 + 3.0625 = 1.6875 3.0625 + -3.5y + y2 = 1.6875 Factor a perfect square on the left side: (y + -1.75)(y + -1.75) = 1.6875 Calculate the square root of the right side: 1.299038106 Break this problem into two subproblems by setting (y + -1.75) equal to 1.299038106 and -1.299038106.Subproblem 1
y + -1.75 = 1.299038106 Simplifying y + -1.75 = 1.299038106 Reorder the terms: -1.75 + y = 1.299038106 Solving -1.75 + y = 1.299038106 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = 1.299038106 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = 1.299038106 + 1.75 y = 1.299038106 + 1.75 Combine like terms: 1.299038106 + 1.75 = 3.049038106 y = 3.049038106 Simplifying y = 3.049038106Subproblem 2
y + -1.75 = -1.299038106 Simplifying y + -1.75 = -1.299038106 Reorder the terms: -1.75 + y = -1.299038106 Solving -1.75 + y = -1.299038106 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = -1.299038106 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = -1.299038106 + 1.75 y = -1.299038106 + 1.75 Combine like terms: -1.299038106 + 1.75 = 0.450961894 y = 0.450961894 Simplifying y = 0.450961894Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.049038106, 0.450961894}
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