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Simplifying 0.5y2 + -1y + -0.027 = 0 Reorder the terms: -0.027 + -1y + 0.5y2 = 0 Solving -0.027 + -1y + 0.5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -0.054 + -2y + y2 = 0 Move the constant term to the right: Add '0.054' to each side of the equation. -0.054 + -2y + 0.054 + y2 = 0 + 0.054 Reorder the terms: -0.054 + 0.054 + -2y + y2 = 0 + 0.054 Combine like terms: -0.054 + 0.054 = 0.000 0.000 + -2y + y2 = 0 + 0.054 -2y + y2 = 0 + 0.054 Combine like terms: 0 + 0.054 = 0.054 -2y + y2 = 0.054 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 0.054 + 1 Reorder the terms: 1 + -2y + y2 = 0.054 + 1 Combine like terms: 0.054 + 1 = 1.054 1 + -2y + y2 = 1.054 Factor a perfect square on the left side: (y + -1)(y + -1) = 1.054 Calculate the square root of the right side: 1.026645021 Break this problem into two subproblems by setting (y + -1) equal to 1.026645021 and -1.026645021.Subproblem 1
y + -1 = 1.026645021 Simplifying y + -1 = 1.026645021 Reorder the terms: -1 + y = 1.026645021 Solving -1 + y = 1.026645021 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 1.026645021 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.026645021 + 1 y = 1.026645021 + 1 Combine like terms: 1.026645021 + 1 = 2.026645021 y = 2.026645021 Simplifying y = 2.026645021Subproblem 2
y + -1 = -1.026645021 Simplifying y + -1 = -1.026645021 Reorder the terms: -1 + y = -1.026645021 Solving -1 + y = -1.026645021 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -1.026645021 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.026645021 + 1 y = -1.026645021 + 1 Combine like terms: -1.026645021 + 1 = -0.026645021 y = -0.026645021 Simplifying y = -0.026645021Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.026645021, -0.026645021}
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