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Simplifying 2y2 + 9y + 55 + -1y2 + 14y + 49 = 0 Reorder the terms: 55 + 49 + 9y + 14y + 2y2 + -1y2 = 0 Combine like terms: 55 + 49 = 104 104 + 9y + 14y + 2y2 + -1y2 = 0 Combine like terms: 9y + 14y = 23y 104 + 23y + 2y2 + -1y2 = 0 Combine like terms: 2y2 + -1y2 = 1y2 104 + 23y + 1y2 = 0 Solving 104 + 23y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-104' to each side of the equation. 104 + 23y + -104 + y2 = 0 + -104 Reorder the terms: 104 + -104 + 23y + y2 = 0 + -104 Combine like terms: 104 + -104 = 0 0 + 23y + y2 = 0 + -104 23y + y2 = 0 + -104 Combine like terms: 0 + -104 = -104 23y + y2 = -104 The y term is 23y. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23y + 132.25 + y2 = -104 + 132.25 Reorder the terms: 132.25 + 23y + y2 = -104 + 132.25 Combine like terms: -104 + 132.25 = 28.25 132.25 + 23y + y2 = 28.25 Factor a perfect square on the left side: (y + 11.5)(y + 11.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (y + 11.5) equal to 5.315072906 and -5.315072906.Subproblem 1
y + 11.5 = 5.315072906 Simplifying y + 11.5 = 5.315072906 Reorder the terms: 11.5 + y = 5.315072906 Solving 11.5 + y = 5.315072906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + y = 5.315072906 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + y = 5.315072906 + -11.5 y = 5.315072906 + -11.5 Combine like terms: 5.315072906 + -11.5 = -6.184927094 y = -6.184927094 Simplifying y = -6.184927094Subproblem 2
y + 11.5 = -5.315072906 Simplifying y + 11.5 = -5.315072906 Reorder the terms: 11.5 + y = -5.315072906 Solving 11.5 + y = -5.315072906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + y = -5.315072906 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + y = -5.315072906 + -11.5 y = -5.315072906 + -11.5 Combine like terms: -5.315072906 + -11.5 = -16.815072906 y = -16.815072906 Simplifying y = -16.815072906Solution
The solution to the problem is based on the solutions from the subproblems. y = {-6.184927094, -16.815072906}
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