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Simplifying x2 + 0.11x + -0.057 = 0 Reorder the terms: -0.057 + 0.11x + x2 = 0 Solving -0.057 + 0.11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.057' to each side of the equation. -0.057 + 0.11x + 0.057 + x2 = 0 + 0.057 Reorder the terms: -0.057 + 0.057 + 0.11x + x2 = 0 + 0.057 Combine like terms: -0.057 + 0.057 = 0.000 0.000 + 0.11x + x2 = 0 + 0.057 0.11x + x2 = 0 + 0.057 Combine like terms: 0 + 0.057 = 0.057 0.11x + x2 = 0.057 The x term is 0.11x. Take half its coefficient (0.055). Square it (0.003025) and add it to both sides. Add '0.003025' to each side of the equation. 0.11x + 0.003025 + x2 = 0.057 + 0.003025 Reorder the terms: 0.003025 + 0.11x + x2 = 0.057 + 0.003025 Combine like terms: 0.057 + 0.003025 = 0.060025 0.003025 + 0.11x + x2 = 0.060025 Factor a perfect square on the left side: (x + 0.055)(x + 0.055) = 0.060025 Calculate the square root of the right side: 0.245 Break this problem into two subproblems by setting (x + 0.055) equal to 0.245 and -0.245.Subproblem 1
x + 0.055 = 0.245 Simplifying x + 0.055 = 0.245 Reorder the terms: 0.055 + x = 0.245 Solving 0.055 + x = 0.245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.055' to each side of the equation. 0.055 + -0.055 + x = 0.245 + -0.055 Combine like terms: 0.055 + -0.055 = 0.000 0.000 + x = 0.245 + -0.055 x = 0.245 + -0.055 Combine like terms: 0.245 + -0.055 = 0.19 x = 0.19 Simplifying x = 0.19Subproblem 2
x + 0.055 = -0.245 Simplifying x + 0.055 = -0.245 Reorder the terms: 0.055 + x = -0.245 Solving 0.055 + x = -0.245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.055' to each side of the equation. 0.055 + -0.055 + x = -0.245 + -0.055 Combine like terms: 0.055 + -0.055 = 0.000 0.000 + x = -0.245 + -0.055 x = -0.245 + -0.055 Combine like terms: -0.245 + -0.055 = -0.3 x = -0.3 Simplifying x = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.19, -0.3}
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