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Simplifying 5 = x(0.11 + x) 5 = (0.11 * x + x * x) 5 = (0.11x + x2) Solving 5 = 0.11x + x2 Solving for variable 'x'. Reorder the terms: 5 + -0.11x + -1x2 = 0.11x + -0.11x + x2 + -1x2 Combine like terms: 0.11x + -0.11x = 0.00 5 + -0.11x + -1x2 = 0.00 + x2 + -1x2 5 + -0.11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + -0.11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 0.11x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.11x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 0.11x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.11x + x2 = 0 + 5 0.11x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.11x + x2 = 5 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 = 5 + 0.003025 Reorder the terms: 0.003025 + 0.11x + x2 = 5 + 0.003025 Combine like terms: 5 + 0.003025 = 5.003025 0.003025 + 0.11x + x2 = 5.003025 Factor a perfect square on the left side: (x + 0.055)(x + 0.055) = 5.003025 Calculate the square root of the right side: 2.236744286 Break this problem into two subproblems by setting (x + 0.055) equal to 2.236744286 and -2.236744286.Subproblem 1
x + 0.055 = 2.236744286 Simplifying x + 0.055 = 2.236744286 Reorder the terms: 0.055 + x = 2.236744286 Solving 0.055 + x = 2.236744286 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 = 2.236744286 + -0.055 Combine like terms: 0.055 + -0.055 = 0.000 0.000 + x = 2.236744286 + -0.055 x = 2.236744286 + -0.055 Combine like terms: 2.236744286 + -0.055 = 2.181744286 x = 2.181744286 Simplifying x = 2.181744286Subproblem 2
x + 0.055 = -2.236744286 Simplifying x + 0.055 = -2.236744286 Reorder the terms: 0.055 + x = -2.236744286 Solving 0.055 + x = -2.236744286 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 = -2.236744286 + -0.055 Combine like terms: 0.055 + -0.055 = 0.000 0.000 + x = -2.236744286 + -0.055 x = -2.236744286 + -0.055 Combine like terms: -2.236744286 + -0.055 = -2.291744286 x = -2.291744286 Simplifying x = -2.291744286Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.181744286, -2.291744286}
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