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Simplifying x2 + -1x = 0.1666 Reorder the terms: -1x + x2 = 0.1666 Solving -1x + x2 = 0.1666 Solving for variable 'x'. Reorder the terms: -0.1666 + -1x + x2 = 0.1666 + -0.1666 Combine like terms: 0.1666 + -0.1666 = 0.0000 -0.1666 + -1x + x2 = 0.0000 Begin completing the square. Move the constant term to the right: Add '0.1666' to each side of the equation. -0.1666 + -1x + 0.1666 + x2 = 0.0000 + 0.1666 Reorder the terms: -0.1666 + 0.1666 + -1x + x2 = 0.0000 + 0.1666 Combine like terms: -0.1666 + 0.1666 = 0.0000 0.0000 + -1x + x2 = 0.0000 + 0.1666 -1x + x2 = 0.0000 + 0.1666 Combine like terms: 0.0000 + 0.1666 = 0.1666 -1x + x2 = 0.1666 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 = 0.1666 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.1666 + 0.25 Combine like terms: 0.1666 + 0.25 = 0.4166 0.25 + -1x + x2 = 0.4166 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.4166 Calculate the square root of the right side: 0.645445583 Break this problem into two subproblems by setting (x + -0.5) equal to 0.645445583 and -0.645445583.Subproblem 1
x + -0.5 = 0.645445583 Simplifying x + -0.5 = 0.645445583 Reorder the terms: -0.5 + x = 0.645445583 Solving -0.5 + x = 0.645445583 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 = 0.645445583 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.645445583 + 0.5 x = 0.645445583 + 0.5 Combine like terms: 0.645445583 + 0.5 = 1.145445583 x = 1.145445583 Simplifying x = 1.145445583Subproblem 2
x + -0.5 = -0.645445583 Simplifying x + -0.5 = -0.645445583 Reorder the terms: -0.5 + x = -0.645445583 Solving -0.5 + x = -0.645445583 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 = -0.645445583 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.645445583 + 0.5 x = -0.645445583 + 0.5 Combine like terms: -0.645445583 + 0.5 = -0.145445583 x = -0.145445583 Simplifying x = -0.145445583Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.145445583, -0.145445583}
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