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Simplifying x2 + -1x + 0.222 = 0 Reorder the terms: 0.222 + -1x + x2 = 0 Solving 0.222 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.222' to each side of the equation. 0.222 + -1x + -0.222 + x2 = 0 + -0.222 Reorder the terms: 0.222 + -0.222 + -1x + x2 = 0 + -0.222 Combine like terms: 0.222 + -0.222 = 0.000 0.000 + -1x + x2 = 0 + -0.222 -1x + x2 = 0 + -0.222 Combine like terms: 0 + -0.222 = -0.222 -1x + x2 = -0.222 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 = -0.222 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.222 + 0.25 Combine like terms: -0.222 + 0.25 = 0.028 0.25 + -1x + x2 = 0.028 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.028 Calculate the square root of the right side: 0.167332005 Break this problem into two subproblems by setting (x + -0.5) equal to 0.167332005 and -0.167332005.Subproblem 1
x + -0.5 = 0.167332005 Simplifying x + -0.5 = 0.167332005 Reorder the terms: -0.5 + x = 0.167332005 Solving -0.5 + x = 0.167332005 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 = 0.167332005 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.167332005 + 0.5 x = 0.167332005 + 0.5 Combine like terms: 0.167332005 + 0.5 = 0.667332005 x = 0.667332005 Simplifying x = 0.667332005Subproblem 2
x + -0.5 = -0.167332005 Simplifying x + -0.5 = -0.167332005 Reorder the terms: -0.5 + x = -0.167332005 Solving -0.5 + x = -0.167332005 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 = -0.167332005 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.167332005 + 0.5 x = -0.167332005 + 0.5 Combine like terms: -0.167332005 + 0.5 = 0.332667995 x = 0.332667995 Simplifying x = 0.332667995Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.667332005, 0.332667995}
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