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Simplifying x2 + -0.6667x + 0.11111 = 0 Reorder the terms: 0.11111 + -0.6667x + x2 = 0 Solving 0.11111 + -0.6667x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.11111' to each side of the equation. 0.11111 + -0.6667x + -0.11111 + x2 = 0 + -0.11111 Reorder the terms: 0.11111 + -0.11111 + -0.6667x + x2 = 0 + -0.11111 Combine like terms: 0.11111 + -0.11111 = 0.00000 0.00000 + -0.6667x + x2 = 0 + -0.11111 -0.6667x + x2 = 0 + -0.11111 Combine like terms: 0 + -0.11111 = -0.11111 -0.6667x + x2 = -0.11111 The x term is -0.6667x. Take half its coefficient (-0.33335). Square it (0.1111222225) and add it to both sides. Add '0.1111222225' to each side of the equation. -0.6667x + 0.1111222225 + x2 = -0.11111 + 0.1111222225 Reorder the terms: 0.1111222225 + -0.6667x + x2 = -0.11111 + 0.1111222225 Combine like terms: -0.11111 + 0.1111222225 = 0.0000122225 0.1111222225 + -0.6667x + x2 = 0.0000122225 Factor a perfect square on the left side: (x + -0.33335)(x + -0.33335) = 0.0000122225 Calculate the square root of the right side: 0.003496069 Break this problem into two subproblems by setting (x + -0.33335) equal to 0.003496069 and -0.003496069.Subproblem 1
x + -0.33335 = 0.003496069 Simplifying x + -0.33335 = 0.003496069 Reorder the terms: -0.33335 + x = 0.003496069 Solving -0.33335 + x = 0.003496069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.33335' to each side of the equation. -0.33335 + 0.33335 + x = 0.003496069 + 0.33335 Combine like terms: -0.33335 + 0.33335 = 0.00000 0.00000 + x = 0.003496069 + 0.33335 x = 0.003496069 + 0.33335 Combine like terms: 0.003496069 + 0.33335 = 0.336846069 x = 0.336846069 Simplifying x = 0.336846069Subproblem 2
x + -0.33335 = -0.003496069 Simplifying x + -0.33335 = -0.003496069 Reorder the terms: -0.33335 + x = -0.003496069 Solving -0.33335 + x = -0.003496069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.33335' to each side of the equation. -0.33335 + 0.33335 + x = -0.003496069 + 0.33335 Combine like terms: -0.33335 + 0.33335 = 0.00000 0.00000 + x = -0.003496069 + 0.33335 x = -0.003496069 + 0.33335 Combine like terms: -0.003496069 + 0.33335 = 0.329853931 x = 0.329853931 Simplifying x = 0.329853931Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.336846069, 0.329853931}
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