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Simplifying y + -1y2 + -65 = -125 Reorder the terms: -65 + y + -1y2 = -125 Solving -65 + y + -1y2 = -125 Solving for variable 'y'. Reorder the terms: -65 + 125 + y + -1y2 = -125 + 125 Combine like terms: -65 + 125 = 60 60 + y + -1y2 = -125 + 125 Combine like terms: -125 + 125 = 0 60 + y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -60 + -1y + y2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -1y + 60 + y2 = 0 + 60 Reorder the terms: -60 + 60 + -1y + y2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -1y + y2 = 0 + 60 -1y + y2 = 0 + 60 Combine like terms: 0 + 60 = 60 -1y + y2 = 60 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 60 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 60 + 0.25 Combine like terms: 60 + 0.25 = 60.25 0.25 + -1y + y2 = 60.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (y + 0.5) equal to 7.762087348 and -7.762087348.Subproblem 1
y + 0.5 = 7.762087348 Simplifying y + 0.5 = 7.762087348 Reorder the terms: 0.5 + y = 7.762087348 Solving 0.5 + y = 7.762087348 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 7.762087348 + -0.5 y = 7.762087348 + -0.5 Combine like terms: 7.762087348 + -0.5 = 7.262087348 y = 7.262087348 Simplifying y = 7.262087348Subproblem 2
y + 0.5 = -7.762087348 Simplifying y + 0.5 = -7.762087348 Reorder the terms: 0.5 + y = -7.762087348 Solving 0.5 + y = -7.762087348 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -7.762087348 + -0.5 y = -7.762087348 + -0.5 Combine like terms: -7.762087348 + -0.5 = -8.262087348 y = -8.262087348 Simplifying y = -8.262087348Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.262087348, -8.262087348}
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