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Simplifying 0.00133 = x + -1x2 Solving 0.00133 = x + -1x2 Solving for variable 'x'. Reorder the terms: 0.00133 + -1x + x2 = x + -1x + -1x2 + x2 Combine like terms: x + -1x = 0 0.00133 + -1x + x2 = 0 + -1x2 + x2 0.00133 + -1x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 0.00133 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-0.00133' to each side of the equation. 0.00133 + -1x + -0.00133 + x2 = 0 + -0.00133 Reorder the terms: 0.00133 + -0.00133 + -1x + x2 = 0 + -0.00133 Combine like terms: 0.00133 + -0.00133 = 0.00000 0.00000 + -1x + x2 = 0 + -0.00133 -1x + x2 = 0 + -0.00133 Combine like terms: 0 + -0.00133 = -0.00133 -1x + x2 = -0.00133 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 = -0.00133 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.00133 + 0.25 Combine like terms: -0.00133 + 0.25 = 0.24867 0.25 + -1x + x2 = 0.24867 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.24867 Calculate the square root of the right side: 0.498668226 Break this problem into two subproblems by setting (x + -0.5) equal to 0.498668226 and -0.498668226.Subproblem 1
x + -0.5 = 0.498668226 Simplifying x + -0.5 = 0.498668226 Reorder the terms: -0.5 + x = 0.498668226 Solving -0.5 + x = 0.498668226 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 = 0.498668226 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.498668226 + 0.5 x = 0.498668226 + 0.5 Combine like terms: 0.498668226 + 0.5 = 0.998668226 x = 0.998668226 Simplifying x = 0.998668226Subproblem 2
x + -0.5 = -0.498668226 Simplifying x + -0.5 = -0.498668226 Reorder the terms: -0.5 + x = -0.498668226 Solving -0.5 + x = -0.498668226 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 = -0.498668226 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.498668226 + 0.5 x = -0.498668226 + 0.5 Combine like terms: -0.498668226 + 0.5 = 0.001331774 x = 0.001331774 Simplifying x = 0.001331774Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.998668226, 0.001331774}
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