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Simplifying y2 + 11y = 30 Reorder the terms: 11y + y2 = 30 Solving 11y + y2 = 30 Solving for variable 'y'. Reorder the terms: -30 + 11y + y2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 11y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 11y + 30 + y2 = 0 + 30 Reorder the terms: -30 + 30 + 11y + y2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 11y + y2 = 0 + 30 11y + y2 = 0 + 30 Combine like terms: 0 + 30 = 30 11y + y2 = 30 The y term is 11y. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11y + 30.25 + y2 = 30 + 30.25 Reorder the terms: 30.25 + 11y + y2 = 30 + 30.25 Combine like terms: 30 + 30.25 = 60.25 30.25 + 11y + y2 = 60.25 Factor a perfect square on the left side: (y + 5.5)(y + 5.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (y + 5.5) equal to 7.762087348 and -7.762087348.Subproblem 1
y + 5.5 = 7.762087348 Simplifying y + 5.5 = 7.762087348 Reorder the terms: 5.5 + y = 7.762087348 Solving 5.5 + y = 7.762087348 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = 7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = 7.762087348 + -5.5 y = 7.762087348 + -5.5 Combine like terms: 7.762087348 + -5.5 = 2.262087348 y = 2.262087348 Simplifying y = 2.262087348Subproblem 2
y + 5.5 = -7.762087348 Simplifying y + 5.5 = -7.762087348 Reorder the terms: 5.5 + y = -7.762087348 Solving 5.5 + y = -7.762087348 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = -7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = -7.762087348 + -5.5 y = -7.762087348 + -5.5 Combine like terms: -7.762087348 + -5.5 = -13.262087348 y = -13.262087348 Simplifying y = -13.262087348Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.262087348, -13.262087348}
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