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Simplifying x2 + -0.667x + 0.111 = 0 Reorder the terms: 0.111 + -0.667x + x2 = 0 Solving 0.111 + -0.667x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.111' to each side of the equation. 0.111 + -0.667x + -0.111 + x2 = 0 + -0.111 Reorder the terms: 0.111 + -0.111 + -0.667x + x2 = 0 + -0.111 Combine like terms: 0.111 + -0.111 = 0.000 0.000 + -0.667x + x2 = 0 + -0.111 -0.667x + x2 = 0 + -0.111 Combine like terms: 0 + -0.111 = -0.111 -0.667x + x2 = -0.111 The x term is -0.667x. Take half its coefficient (-0.3335). Square it (0.11122225) and add it to both sides. Add '0.11122225' to each side of the equation. -0.667x + 0.11122225 + x2 = -0.111 + 0.11122225 Reorder the terms: 0.11122225 + -0.667x + x2 = -0.111 + 0.11122225 Combine like terms: -0.111 + 0.11122225 = 0.00022225 0.11122225 + -0.667x + x2 = 0.00022225 Factor a perfect square on the left side: (x + -0.3335)(x + -0.3335) = 0.00022225 Calculate the square root of the right side: 0.014908052 Break this problem into two subproblems by setting (x + -0.3335) equal to 0.014908052 and -0.014908052.Subproblem 1
x + -0.3335 = 0.014908052 Simplifying x + -0.3335 = 0.014908052 Reorder the terms: -0.3335 + x = 0.014908052 Solving -0.3335 + x = 0.014908052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3335' to each side of the equation. -0.3335 + 0.3335 + x = 0.014908052 + 0.3335 Combine like terms: -0.3335 + 0.3335 = 0.0000 0.0000 + x = 0.014908052 + 0.3335 x = 0.014908052 + 0.3335 Combine like terms: 0.014908052 + 0.3335 = 0.348408052 x = 0.348408052 Simplifying x = 0.348408052Subproblem 2
x + -0.3335 = -0.014908052 Simplifying x + -0.3335 = -0.014908052 Reorder the terms: -0.3335 + x = -0.014908052 Solving -0.3335 + x = -0.014908052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3335' to each side of the equation. -0.3335 + 0.3335 + x = -0.014908052 + 0.3335 Combine like terms: -0.3335 + 0.3335 = 0.0000 0.0000 + x = -0.014908052 + 0.3335 x = -0.014908052 + 0.3335 Combine like terms: -0.014908052 + 0.3335 = 0.318591948 x = 0.318591948 Simplifying x = 0.318591948Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.348408052, 0.318591948}
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