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Simplifying y2 + 9y = 8 Reorder the terms: 9y + y2 = 8 Solving 9y + y2 = 8 Solving for variable 'y'. Reorder the terms: -8 + 9y + y2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 9y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 9y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + 9y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 9y + y2 = 0 + 8 9y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 9y + y2 = 8 The y term is 9y. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9y + 20.25 + y2 = 8 + 20.25 Reorder the terms: 20.25 + 9y + y2 = 8 + 20.25 Combine like terms: 8 + 20.25 = 28.25 20.25 + 9y + y2 = 28.25 Factor a perfect square on the left side: (y + 4.5)(y + 4.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (y + 4.5) equal to 5.315072906 and -5.315072906.Subproblem 1
y + 4.5 = 5.315072906 Simplifying y + 4.5 = 5.315072906 Reorder the terms: 4.5 + y = 5.315072906 Solving 4.5 + y = 5.315072906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = 5.315072906 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = 5.315072906 + -4.5 y = 5.315072906 + -4.5 Combine like terms: 5.315072906 + -4.5 = 0.815072906 y = 0.815072906 Simplifying y = 0.815072906Subproblem 2
y + 4.5 = -5.315072906 Simplifying y + 4.5 = -5.315072906 Reorder the terms: 4.5 + y = -5.315072906 Solving 4.5 + y = -5.315072906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = -5.315072906 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = -5.315072906 + -4.5 y = -5.315072906 + -4.5 Combine like terms: -5.315072906 + -4.5 = -9.815072906 y = -9.815072906 Simplifying y = -9.815072906Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.815072906, -9.815072906}
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