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Simplifying 100x + 432979.5918x2 = 0.6220 Solving 100x + 432979.5918x2 = 0.6220 Solving for variable 'x'. Reorder the terms: -0.6220 + 100x + 432979.5918x2 = 0.6220 + -0.6220 Combine like terms: 0.6220 + -0.6220 = 0.0000 -0.6220 + 100x + 432979.5918x2 = 0.0000 Begin completing the square. Divide all terms by 432979.5918 the coefficient of the squared term: Divide each side by '432979.5918'. -0.000001436557315 + 0.0002309577677x + x2 = 0 Move the constant term to the right: Add '0.000001436557315' to each side of the equation. -0.000001436557315 + 0.0002309577677x + 0.000001436557315 + x2 = 0 + 0.000001436557315 Reorder the terms: -0.000001436557315 + 0.000001436557315 + 0.0002309577677x + x2 = 0 + 0.000001436557315 Combine like terms: -0.000001436557315 + 0.000001436557315 = 0.000000000000000 0.000000000000000 + 0.0002309577677x + x2 = 0 + 0.000001436557315 0.0002309577677x + x2 = 0 + 0.000001436557315 Combine like terms: 0 + 0.000001436557315 = 0.000001436557315 0.0002309577677x + x2 = 0.000001436557315 The x term is 0.0002309577677x. Take half its coefficient (0.0001154788839). Square it (0.00000001333537263) and add it to both sides. Add '0.00000001333537263' to each side of the equation. 0.0002309577677x + 0.00000001333537263 + x2 = 0.000001436557315 + 0.00000001333537263 Reorder the terms: 0.00000001333537263 + 0.0002309577677x + x2 = 0.000001436557315 + 0.00000001333537263 Combine like terms: 0.000001436557315 + 0.00000001333537263 = 0.00000144989268763 0.00000001333537263 + 0.0002309577677x + x2 = 0.00000144989268763 Factor a perfect square on the left side: (x + 0.0001154788839)(x + 0.0001154788839) = 0.00000144989268763 Calculate the square root of the right side: 0.001204115 Break this problem into two subproblems by setting (x + 0.0001154788839) equal to 0.001204115 and -0.001204115.Subproblem 1
x + 0.0001154788839 = 0.001204115 Simplifying x + 0.0001154788839 = 0.001204115 Reorder the terms: 0.0001154788839 + x = 0.001204115 Solving 0.0001154788839 + x = 0.001204115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0001154788839' to each side of the equation. 0.0001154788839 + -0.0001154788839 + x = 0.001204115 + -0.0001154788839 Combine like terms: 0.0001154788839 + -0.0001154788839 = 0.0000000000000 0.0000000000000 + x = 0.001204115 + -0.0001154788839 x = 0.001204115 + -0.0001154788839 Combine like terms: 0.001204115 + -0.0001154788839 = 0.0010886361161 x = 0.0010886361161 Simplifying x = 0.0010886361161Subproblem 2
x + 0.0001154788839 = -0.001204115 Simplifying x + 0.0001154788839 = -0.001204115 Reorder the terms: 0.0001154788839 + x = -0.001204115 Solving 0.0001154788839 + x = -0.001204115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0001154788839' to each side of the equation. 0.0001154788839 + -0.0001154788839 + x = -0.001204115 + -0.0001154788839 Combine like terms: 0.0001154788839 + -0.0001154788839 = 0.0000000000000 0.0000000000000 + x = -0.001204115 + -0.0001154788839 x = -0.001204115 + -0.0001154788839 Combine like terms: -0.001204115 + -0.0001154788839 = -0.0013195938839 x = -0.0013195938839 Simplifying x = -0.0013195938839Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0010886361161, -0.0013195938839}
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