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Simplifying 0.055x2 + 1.1x = 40 Reorder the terms: 1.1x + 0.055x2 = 40 Solving 1.1x + 0.055x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + 1.1x + 0.055x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 1.1x + 0.055x2 = 0 Begin completing the square. Divide all terms by 0.055 the coefficient of the squared term: Divide each side by '0.055'. -727.2727273 + 20x + x2 = 0 Move the constant term to the right: Add '727.2727273' to each side of the equation. -727.2727273 + 20x + 727.2727273 + x2 = 0 + 727.2727273 Reorder the terms: -727.2727273 + 727.2727273 + 20x + x2 = 0 + 727.2727273 Combine like terms: -727.2727273 + 727.2727273 = 0.0000000 0.0000000 + 20x + x2 = 0 + 727.2727273 20x + x2 = 0 + 727.2727273 Combine like terms: 0 + 727.2727273 = 727.2727273 20x + x2 = 727.2727273 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 727.2727273 + 100 Reorder the terms: 100 + 20x + x2 = 727.2727273 + 100 Combine like terms: 727.2727273 + 100 = 827.2727273 100 + 20x + x2 = 827.2727273 Factor a perfect square on the left side: (x + 10)(x + 10) = 827.2727273 Calculate the square root of the right side: 28.762349127 Break this problem into two subproblems by setting (x + 10) equal to 28.762349127 and -28.762349127.Subproblem 1
x + 10 = 28.762349127 Simplifying x + 10 = 28.762349127 Reorder the terms: 10 + x = 28.762349127 Solving 10 + x = 28.762349127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 28.762349127 + -10 Combine like terms: 10 + -10 = 0 0 + x = 28.762349127 + -10 x = 28.762349127 + -10 Combine like terms: 28.762349127 + -10 = 18.762349127 x = 18.762349127 Simplifying x = 18.762349127Subproblem 2
x + 10 = -28.762349127 Simplifying x + 10 = -28.762349127 Reorder the terms: 10 + x = -28.762349127 Solving 10 + x = -28.762349127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -28.762349127 + -10 Combine like terms: 10 + -10 = 0 0 + x = -28.762349127 + -10 x = -28.762349127 + -10 Combine like terms: -28.762349127 + -10 = -38.762349127 x = -38.762349127 Simplifying x = -38.762349127Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.762349127, -38.762349127}
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