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Simplifying 2Y2 + 19Y + 35 = Y2 + 49 Reorder the terms: 35 + 19Y + 2Y2 = Y2 + 49 Reorder the terms: 35 + 19Y + 2Y2 = 49 + Y2 Solving 35 + 19Y + 2Y2 = 49 + Y2 Solving for variable 'Y'. Reorder the terms: 35 + -49 + 19Y + 2Y2 + -1Y2 = 49 + Y2 + -49 + -1Y2 Combine like terms: 35 + -49 = -14 -14 + 19Y + 2Y2 + -1Y2 = 49 + Y2 + -49 + -1Y2 Combine like terms: 2Y2 + -1Y2 = 1Y2 -14 + 19Y + 1Y2 = 49 + Y2 + -49 + -1Y2 Reorder the terms: -14 + 19Y + 1Y2 = 49 + -49 + Y2 + -1Y2 Combine like terms: 49 + -49 = 0 -14 + 19Y + 1Y2 = 0 + Y2 + -1Y2 -14 + 19Y + 1Y2 = Y2 + -1Y2 Combine like terms: Y2 + -1Y2 = 0 -14 + 19Y + 1Y2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 19Y + 14 + Y2 = 0 + 14 Reorder the terms: -14 + 14 + 19Y + Y2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 19Y + Y2 = 0 + 14 19Y + Y2 = 0 + 14 Combine like terms: 0 + 14 = 14 19Y + Y2 = 14 The Y term is 19Y. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19Y + 90.25 + Y2 = 14 + 90.25 Reorder the terms: 90.25 + 19Y + Y2 = 14 + 90.25 Combine like terms: 14 + 90.25 = 104.25 90.25 + 19Y + Y2 = 104.25 Factor a perfect square on the left side: (Y + 9.5)(Y + 9.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (Y + 9.5) equal to 10.210288928 and -10.210288928.Subproblem 1
Y + 9.5 = 10.210288928 Simplifying Y + 9.5 = 10.210288928 Reorder the terms: 9.5 + Y = 10.210288928 Solving 9.5 + Y = 10.210288928 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + Y = 10.210288928 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + Y = 10.210288928 + -9.5 Y = 10.210288928 + -9.5 Combine like terms: 10.210288928 + -9.5 = 0.710288928 Y = 0.710288928 Simplifying Y = 0.710288928Subproblem 2
Y + 9.5 = -10.210288928 Simplifying Y + 9.5 = -10.210288928 Reorder the terms: 9.5 + Y = -10.210288928 Solving 9.5 + Y = -10.210288928 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + Y = -10.210288928 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + Y = -10.210288928 + -9.5 Y = -10.210288928 + -9.5 Combine like terms: -10.210288928 + -9.5 = -19.710288928 Y = -19.710288928 Simplifying Y = -19.710288928Solution
The solution to the problem is based on the solutions from the subproblems. Y = {0.710288928, -19.710288928}
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