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Simplifying -11x + -61 + 18x2 = 0 Reorder the terms: -61 + -11x + 18x2 = 0 Solving -61 + -11x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -3.388888889 + -0.6111111111x + x2 = 0 Move the constant term to the right: Add '3.388888889' to each side of the equation. -3.388888889 + -0.6111111111x + 3.388888889 + x2 = 0 + 3.388888889 Reorder the terms: -3.388888889 + 3.388888889 + -0.6111111111x + x2 = 0 + 3.388888889 Combine like terms: -3.388888889 + 3.388888889 = 0.000000000 0.000000000 + -0.6111111111x + x2 = 0 + 3.388888889 -0.6111111111x + x2 = 0 + 3.388888889 Combine like terms: 0 + 3.388888889 = 3.388888889 -0.6111111111x + x2 = 3.388888889 The x term is -0.6111111111x. Take half its coefficient (-0.3055555556). Square it (0.09336419756) and add it to both sides. Add '0.09336419756' to each side of the equation. -0.6111111111x + 0.09336419756 + x2 = 3.388888889 + 0.09336419756 Reorder the terms: 0.09336419756 + -0.6111111111x + x2 = 3.388888889 + 0.09336419756 Combine like terms: 3.388888889 + 0.09336419756 = 3.48225308656 0.09336419756 + -0.6111111111x + x2 = 3.48225308656 Factor a perfect square on the left side: (x + -0.3055555556)(x + -0.3055555556) = 3.48225308656 Calculate the square root of the right side: 1.866079603 Break this problem into two subproblems by setting (x + -0.3055555556) equal to 1.866079603 and -1.866079603.Subproblem 1
x + -0.3055555556 = 1.866079603 Simplifying x + -0.3055555556 = 1.866079603 Reorder the terms: -0.3055555556 + x = 1.866079603 Solving -0.3055555556 + x = 1.866079603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3055555556' to each side of the equation. -0.3055555556 + 0.3055555556 + x = 1.866079603 + 0.3055555556 Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000 0.0000000000 + x = 1.866079603 + 0.3055555556 x = 1.866079603 + 0.3055555556 Combine like terms: 1.866079603 + 0.3055555556 = 2.1716351586 x = 2.1716351586 Simplifying x = 2.1716351586Subproblem 2
x + -0.3055555556 = -1.866079603 Simplifying x + -0.3055555556 = -1.866079603 Reorder the terms: -0.3055555556 + x = -1.866079603 Solving -0.3055555556 + x = -1.866079603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3055555556' to each side of the equation. -0.3055555556 + 0.3055555556 + x = -1.866079603 + 0.3055555556 Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000 0.0000000000 + x = -1.866079603 + 0.3055555556 x = -1.866079603 + 0.3055555556 Combine like terms: -1.866079603 + 0.3055555556 = -1.5605240474 x = -1.5605240474 Simplifying x = -1.5605240474Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1716351586, -1.5605240474}
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