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Simplifying 2y2 + -8y + 15 + -1y2 + 36y + -12 = 0 Reorder the terms: 15 + -12 + -8y + 36y + 2y2 + -1y2 = 0 Combine like terms: 15 + -12 = 3 3 + -8y + 36y + 2y2 + -1y2 = 0 Combine like terms: -8y + 36y = 28y 3 + 28y + 2y2 + -1y2 = 0 Combine like terms: 2y2 + -1y2 = 1y2 3 + 28y + 1y2 = 0 Solving 3 + 28y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 28y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + 28y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 28y + y2 = 0 + -3 28y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 28y + y2 = -3 The y term is 28y. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28y + 196 + y2 = -3 + 196 Reorder the terms: 196 + 28y + y2 = -3 + 196 Combine like terms: -3 + 196 = 193 196 + 28y + y2 = 193 Factor a perfect square on the left side: (y + 14)(y + 14) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (y + 14) equal to 13.892443989 and -13.892443989.Subproblem 1
y + 14 = 13.892443989 Simplifying y + 14 = 13.892443989 Reorder the terms: 14 + y = 13.892443989 Solving 14 + y = 13.892443989 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = 13.892443989 + -14 Combine like terms: 14 + -14 = 0 0 + y = 13.892443989 + -14 y = 13.892443989 + -14 Combine like terms: 13.892443989 + -14 = -0.107556011 y = -0.107556011 Simplifying y = -0.107556011Subproblem 2
y + 14 = -13.892443989 Simplifying y + 14 = -13.892443989 Reorder the terms: 14 + y = -13.892443989 Solving 14 + y = -13.892443989 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = -13.892443989 + -14 Combine like terms: 14 + -14 = 0 0 + y = -13.892443989 + -14 y = -13.892443989 + -14 Combine like terms: -13.892443989 + -14 = -27.892443989 y = -27.892443989 Simplifying y = -27.892443989Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.107556011, -27.892443989}
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