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Simplifying y2 + y + -1296 = 0 Reorder the terms: -1296 + y + y2 = 0 Solving -1296 + y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '1296' to each side of the equation. -1296 + y + 1296 + y2 = 0 + 1296 Reorder the terms: -1296 + 1296 + y + y2 = 0 + 1296 Combine like terms: -1296 + 1296 = 0 0 + y + y2 = 0 + 1296 y + y2 = 0 + 1296 Combine like terms: 0 + 1296 = 1296 y + y2 = 1296 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. y + 0.25 + y2 = 1296 + 0.25 Reorder the terms: 0.25 + y + y2 = 1296 + 0.25 Combine like terms: 1296 + 0.25 = 1296.25 0.25 + y + y2 = 1296.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 1296.25 Calculate the square root of the right side: 36.003472055 Break this problem into two subproblems by setting (y + 0.5) equal to 36.003472055 and -36.003472055.Subproblem 1
y + 0.5 = 36.003472055 Simplifying y + 0.5 = 36.003472055 Reorder the terms: 0.5 + y = 36.003472055 Solving 0.5 + y = 36.003472055 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 36.003472055 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 36.003472055 + -0.5 y = 36.003472055 + -0.5 Combine like terms: 36.003472055 + -0.5 = 35.503472055 y = 35.503472055 Simplifying y = 35.503472055Subproblem 2
y + 0.5 = -36.003472055 Simplifying y + 0.5 = -36.003472055 Reorder the terms: 0.5 + y = -36.003472055 Solving 0.5 + y = -36.003472055 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -36.003472055 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -36.003472055 + -0.5 y = -36.003472055 + -0.5 Combine like terms: -36.003472055 + -0.5 = -36.503472055 y = -36.503472055 Simplifying y = -36.503472055Solution
The solution to the problem is based on the solutions from the subproblems. y = {35.503472055, -36.503472055}
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