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Simplifying x2 + -6x + (0.222) = 0 x2 + -6x + 0.222 = 0 Reorder the terms: 0.222 + -6x + x2 = 0 Solving 0.222 + -6x + 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 + -6x + -0.222 + x2 = 0 + -0.222 Reorder the terms: 0.222 + -0.222 + -6x + x2 = 0 + -0.222 Combine like terms: 0.222 + -0.222 = 0.000 0.000 + -6x + x2 = 0 + -0.222 -6x + x2 = 0 + -0.222 Combine like terms: 0 + -0.222 = -0.222 -6x + x2 = -0.222 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -0.222 + 9 Reorder the terms: 9 + -6x + x2 = -0.222 + 9 Combine like terms: -0.222 + 9 = 8.778 9 + -6x + x2 = 8.778 Factor a perfect square on the left side: (x + -3)(x + -3) = 8.778 Calculate the square root of the right side: 2.962768975 Break this problem into two subproblems by setting (x + -3) equal to 2.962768975 and -2.962768975.Subproblem 1
x + -3 = 2.962768975 Simplifying x + -3 = 2.962768975 Reorder the terms: -3 + x = 2.962768975 Solving -3 + x = 2.962768975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.962768975 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.962768975 + 3 x = 2.962768975 + 3 Combine like terms: 2.962768975 + 3 = 5.962768975 x = 5.962768975 Simplifying x = 5.962768975Subproblem 2
x + -3 = -2.962768975 Simplifying x + -3 = -2.962768975 Reorder the terms: -3 + x = -2.962768975 Solving -3 + x = -2.962768975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.962768975 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.962768975 + 3 x = -2.962768975 + 3 Combine like terms: -2.962768975 + 3 = 0.037231025 x = 0.037231025 Simplifying x = 0.037231025Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.962768975, 0.037231025}
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