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Simplifying x * x + -1x = 0.038 Multiply x * x x2 + -1x = 0.038 Reorder the terms: -1x + x2 = 0.038 Solving -1x + x2 = 0.038 Solving for variable 'x'. Reorder the terms: -0.038 + -1x + x2 = 0.038 + -0.038 Combine like terms: 0.038 + -0.038 = 0.000 -0.038 + -1x + x2 = 0.000 Begin completing the square. 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 -1x. 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 = 0.288 0.25 + -1x + x2 = 0.288 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.288 Calculate the square root of the right side: 0.536656315 Break this problem into two subproblems by setting (x + -0.5) equal to 0.536656315 and -0.536656315.Subproblem 1
x + -0.5 = 0.536656315 Simplifying x + -0.5 = 0.536656315 Reorder the terms: -0.5 + x = 0.536656315 Solving -0.5 + x = 0.536656315 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 = 0.536656315 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.536656315 + 0.5 x = 0.536656315 + 0.5 Combine like terms: 0.536656315 + 0.5 = 1.036656315 x = 1.036656315 Simplifying x = 1.036656315Subproblem 2
x + -0.5 = -0.536656315 Simplifying x + -0.5 = -0.536656315 Reorder the terms: -0.5 + x = -0.536656315 Solving -0.5 + x = -0.536656315 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 = -0.536656315 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.536656315 + 0.5 x = -0.536656315 + 0.5 Combine like terms: -0.536656315 + 0.5 = -0.036656315 x = -0.036656315 Simplifying x = -0.036656315Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.036656315, -0.036656315}
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