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Simplifying x + -1x2 = 0.038 Solving x + -1x2 = 0.038 Solving for variable 'x'. Reorder the terms: -0.038 + x + -1x2 = 0.038 + -0.038 Combine like terms: 0.038 + -0.038 = 0.000 -0.038 + x + -1x2 = 0.000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.038 + -1x + x2 = 0.000 Move the constant term to the right: Add '-0.038' to each side of the equation. 0.038 + -1x + -0.038 + x2 = 0.000 + -0.038 Reorder the terms: 0.038 + -0.038 + -1x + x2 = 0.000 + -0.038 Combine like terms: 0.038 + -0.038 = 0.000 0.000 + -1x + x2 = 0.000 + -0.038 -1x + x2 = 0.000 + -0.038 Combine like terms: 0.000 + -0.038 = -0.038 -1x + x2 = -0.038 The x term is x. 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. -1x + 0.25 + x2 = -0.038 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.038 + 0.25 Combine like terms: -0.038 + 0.25 = 0.212 0.25 + -1x + x2 = 0.212 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.212 Calculate the square root of the right side: 0.460434577 Break this problem into two subproblems by setting (x + 0.5) equal to 0.460434577 and -0.460434577.Subproblem 1
x + 0.5 = 0.460434577 Simplifying x + 0.5 = 0.460434577 Reorder the terms: 0.5 + x = 0.460434577 Solving 0.5 + x = 0.460434577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.460434577 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.460434577 + -0.5 x = 0.460434577 + -0.5 Combine like terms: 0.460434577 + -0.5 = -0.039565423 x = -0.039565423 Simplifying x = -0.039565423Subproblem 2
x + 0.5 = -0.460434577 Simplifying x + 0.5 = -0.460434577 Reorder the terms: 0.5 + x = -0.460434577 Solving 0.5 + x = -0.460434577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.460434577 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.460434577 + -0.5 x = -0.460434577 + -0.5 Combine like terms: -0.460434577 + -0.5 = -0.960434577 x = -0.960434577 Simplifying x = -0.960434577Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.039565423, -0.960434577}
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