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Simplifying x2 + 27x + 96 = 0 Reorder the terms: 96 + 27x + x2 = 0 Solving 96 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-96' to each side of the equation. 96 + 27x + -96 + x2 = 0 + -96 Reorder the terms: 96 + -96 + 27x + x2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + 27x + x2 = 0 + -96 27x + x2 = 0 + -96 Combine like terms: 0 + -96 = -96 27x + x2 = -96 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = -96 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -96 + 182.25 Combine like terms: -96 + 182.25 = 86.25 182.25 + 27x + x2 = 86.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + 13.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + 13.5 = 9.287087811 Simplifying x + 13.5 = 9.287087811 Reorder the terms: 13.5 + x = 9.287087811 Solving 13.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 9.287087811 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 9.287087811 + -13.5 x = 9.287087811 + -13.5 Combine like terms: 9.287087811 + -13.5 = -4.212912189 x = -4.212912189 Simplifying x = -4.212912189Subproblem 2
x + 13.5 = -9.287087811 Simplifying x + 13.5 = -9.287087811 Reorder the terms: 13.5 + x = -9.287087811 Solving 13.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -9.287087811 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -9.287087811 + -13.5 x = -9.287087811 + -13.5 Combine like terms: -9.287087811 + -13.5 = -22.787087811 x = -22.787087811 Simplifying x = -22.787087811Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.212912189, -22.787087811}
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