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Simplifying 18x2 + -11x + -6 = 0 Reorder the terms: -6 + -11x + 18x2 = 0 Solving -6 + -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'. -0.3333333333 + -0.6111111111x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.6111111111x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.6111111111x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.6111111111x + x2 = 0 + 0.3333333333 -0.6111111111x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.6111111111x + x2 = 0.3333333333 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 = 0.3333333333 + 0.09336419756 Reorder the terms: 0.09336419756 + -0.6111111111x + x2 = 0.3333333333 + 0.09336419756 Combine like terms: 0.3333333333 + 0.09336419756 = 0.42669753086 0.09336419756 + -0.6111111111x + x2 = 0.42669753086 Factor a perfect square on the left side: (x + -0.3055555556)(x + -0.3055555556) = 0.42669753086 Calculate the square root of the right side: 0.65322089 Break this problem into two subproblems by setting (x + -0.3055555556) equal to 0.65322089 and -0.65322089.Subproblem 1
x + -0.3055555556 = 0.65322089 Simplifying x + -0.3055555556 = 0.65322089 Reorder the terms: -0.3055555556 + x = 0.65322089 Solving -0.3055555556 + x = 0.65322089 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 = 0.65322089 + 0.3055555556 Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000 0.0000000000 + x = 0.65322089 + 0.3055555556 x = 0.65322089 + 0.3055555556 Combine like terms: 0.65322089 + 0.3055555556 = 0.9587764456 x = 0.9587764456 Simplifying x = 0.9587764456Subproblem 2
x + -0.3055555556 = -0.65322089 Simplifying x + -0.3055555556 = -0.65322089 Reorder the terms: -0.3055555556 + x = -0.65322089 Solving -0.3055555556 + x = -0.65322089 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 = -0.65322089 + 0.3055555556 Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000 0.0000000000 + x = -0.65322089 + 0.3055555556 x = -0.65322089 + 0.3055555556 Combine like terms: -0.65322089 + 0.3055555556 = -0.3476653344 x = -0.3476653344 Simplifying x = -0.3476653344Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9587764456, -0.3476653344}
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