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Simplifying 0.000018x2 + 0.007427x + -0.0217 = 0 Reorder the terms: -0.0217 + 0.007427x + 0.000018x2 = 0 Solving -0.0217 + 0.007427x + 0.000018x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.000018 the coefficient of the squared term: Divide each side by '0.000018'. -1205.555556 + 412.6111111x + x2 = 0 Move the constant term to the right: Add '1205.555556' to each side of the equation. -1205.555556 + 412.6111111x + 1205.555556 + x2 = 0 + 1205.555556 Reorder the terms: -1205.555556 + 1205.555556 + 412.6111111x + x2 = 0 + 1205.555556 Combine like terms: -1205.555556 + 1205.555556 = 0.000000 0.000000 + 412.6111111x + x2 = 0 + 1205.555556 412.6111111x + x2 = 0 + 1205.555556 Combine like terms: 0 + 1205.555556 = 1205.555556 412.6111111x + x2 = 1205.555556 The x term is 412.6111111x. Take half its coefficient (206.3055556). Square it (42561.98227) and add it to both sides. Add '42561.98227' to each side of the equation. 412.6111111x + 42561.98227 + x2 = 1205.555556 + 42561.98227 Reorder the terms: 42561.98227 + 412.6111111x + x2 = 1205.555556 + 42561.98227 Combine like terms: 1205.555556 + 42561.98227 = 43767.537826 42561.98227 + 412.6111111x + x2 = 43767.537826 Factor a perfect square on the left side: (x + 206.3055556)(x + 206.3055556) = 43767.537826 Calculate the square root of the right side: 209.206925856 Break this problem into two subproblems by setting (x + 206.3055556) equal to 209.206925856 and -209.206925856.Subproblem 1
x + 206.3055556 = 209.206925856 Simplifying x + 206.3055556 = 209.206925856 Reorder the terms: 206.3055556 + x = 209.206925856 Solving 206.3055556 + x = 209.206925856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-206.3055556' to each side of the equation. 206.3055556 + -206.3055556 + x = 209.206925856 + -206.3055556 Combine like terms: 206.3055556 + -206.3055556 = 0.0000000 0.0000000 + x = 209.206925856 + -206.3055556 x = 209.206925856 + -206.3055556 Combine like terms: 209.206925856 + -206.3055556 = 2.901370256 x = 2.901370256 Simplifying x = 2.901370256Subproblem 2
x + 206.3055556 = -209.206925856 Simplifying x + 206.3055556 = -209.206925856 Reorder the terms: 206.3055556 + x = -209.206925856 Solving 206.3055556 + x = -209.206925856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-206.3055556' to each side of the equation. 206.3055556 + -206.3055556 + x = -209.206925856 + -206.3055556 Combine like terms: 206.3055556 + -206.3055556 = 0.0000000 0.0000000 + x = -209.206925856 + -206.3055556 x = -209.206925856 + -206.3055556 Combine like terms: -209.206925856 + -206.3055556 = -415.512481456 x = -415.512481456 Simplifying x = -415.512481456Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.901370256, -415.512481456}
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