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Simplifying 116666.667 = x2 + -333.333x Reorder the terms: 116666.667 = -333.333x + x2 Solving 116666.667 = -333.333x + x2 Solving for variable 'x'. Reorder the terms: 116666.667 + 333.333x + -1x2 = -333.333x + 333.333x + x2 + -1x2 Combine like terms: -333.333x + 333.333x = 0.000 116666.667 + 333.333x + -1x2 = 0.000 + x2 + -1x2 116666.667 + 333.333x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 116666.667 + 333.333x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -116666.667 + -333.333x + x2 = 0 Move the constant term to the right: Add '116666.667' to each side of the equation. -116666.667 + -333.333x + 116666.667 + x2 = 0 + 116666.667 Reorder the terms: -116666.667 + 116666.667 + -333.333x + x2 = 0 + 116666.667 Combine like terms: -116666.667 + 116666.667 = 0.000 0.000 + -333.333x + x2 = 0 + 116666.667 -333.333x + x2 = 0 + 116666.667 Combine like terms: 0 + 116666.667 = 116666.667 -333.333x + x2 = 116666.667 The x term is -333.333x. Take half its coefficient (-166.6665). Square it (27777.72222) and add it to both sides. Add '27777.72222' to each side of the equation. -333.333x + 27777.72222 + x2 = 116666.667 + 27777.72222 Reorder the terms: 27777.72222 + -333.333x + x2 = 116666.667 + 27777.72222 Combine like terms: 116666.667 + 27777.72222 = 144444.38922 27777.72222 + -333.333x + x2 = 144444.38922 Factor a perfect square on the left side: (x + -166.6665)(x + -166.6665) = 144444.38922 Calculate the square root of the right side: 380.05840238 Break this problem into two subproblems by setting (x + -166.6665) equal to 380.05840238 and -380.05840238.Subproblem 1
x + -166.6665 = 380.05840238 Simplifying x + -166.6665 = 380.05840238 Reorder the terms: -166.6665 + x = 380.05840238 Solving -166.6665 + x = 380.05840238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '166.6665' to each side of the equation. -166.6665 + 166.6665 + x = 380.05840238 + 166.6665 Combine like terms: -166.6665 + 166.6665 = 0.0000 0.0000 + x = 380.05840238 + 166.6665 x = 380.05840238 + 166.6665 Combine like terms: 380.05840238 + 166.6665 = 546.72490238 x = 546.72490238 Simplifying x = 546.72490238Subproblem 2
x + -166.6665 = -380.05840238 Simplifying x + -166.6665 = -380.05840238 Reorder the terms: -166.6665 + x = -380.05840238 Solving -166.6665 + x = -380.05840238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '166.6665' to each side of the equation. -166.6665 + 166.6665 + x = -380.05840238 + 166.6665 Combine like terms: -166.6665 + 166.6665 = 0.0000 0.0000 + x = -380.05840238 + 166.6665 x = -380.05840238 + 166.6665 Combine like terms: -380.05840238 + 166.6665 = -213.39190238 x = -213.39190238 Simplifying x = -213.39190238Solution
The solution to the problem is based on the solutions from the subproblems. x = {546.72490238, -213.39190238}
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