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Simplifying 22x2 + -3x + -27 = 0 Reorder the terms: -27 + -3x + 22x2 = 0 Solving -27 + -3x + 22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -1.227272727 + -0.1363636364x + x2 = 0 Move the constant term to the right: Add '1.227272727' to each side of the equation. -1.227272727 + -0.1363636364x + 1.227272727 + x2 = 0 + 1.227272727 Reorder the terms: -1.227272727 + 1.227272727 + -0.1363636364x + x2 = 0 + 1.227272727 Combine like terms: -1.227272727 + 1.227272727 = 0.000000000 0.000000000 + -0.1363636364x + x2 = 0 + 1.227272727 -0.1363636364x + x2 = 0 + 1.227272727 Combine like terms: 0 + 1.227272727 = 1.227272727 -0.1363636364x + x2 = 1.227272727 The x term is -0.1363636364x. Take half its coefficient (-0.0681818182). Square it (0.004648760333) and add it to both sides. Add '0.004648760333' to each side of the equation. -0.1363636364x + 0.004648760333 + x2 = 1.227272727 + 0.004648760333 Reorder the terms: 0.004648760333 + -0.1363636364x + x2 = 1.227272727 + 0.004648760333 Combine like terms: 1.227272727 + 0.004648760333 = 1.231921487333 0.004648760333 + -0.1363636364x + x2 = 1.231921487333 Factor a perfect square on the left side: (x + -0.0681818182)(x + -0.0681818182) = 1.231921487333 Calculate the square root of the right side: 1.109919586 Break this problem into two subproblems by setting (x + -0.0681818182) equal to 1.109919586 and -1.109919586.Subproblem 1
x + -0.0681818182 = 1.109919586 Simplifying x + -0.0681818182 = 1.109919586 Reorder the terms: -0.0681818182 + x = 1.109919586 Solving -0.0681818182 + x = 1.109919586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0681818182' to each side of the equation. -0.0681818182 + 0.0681818182 + x = 1.109919586 + 0.0681818182 Combine like terms: -0.0681818182 + 0.0681818182 = 0.0000000000 0.0000000000 + x = 1.109919586 + 0.0681818182 x = 1.109919586 + 0.0681818182 Combine like terms: 1.109919586 + 0.0681818182 = 1.1781014042 x = 1.1781014042 Simplifying x = 1.1781014042Subproblem 2
x + -0.0681818182 = -1.109919586 Simplifying x + -0.0681818182 = -1.109919586 Reorder the terms: -0.0681818182 + x = -1.109919586 Solving -0.0681818182 + x = -1.109919586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0681818182' to each side of the equation. -0.0681818182 + 0.0681818182 + x = -1.109919586 + 0.0681818182 Combine like terms: -0.0681818182 + 0.0681818182 = 0.0000000000 0.0000000000 + x = -1.109919586 + 0.0681818182 x = -1.109919586 + 0.0681818182 Combine like terms: -1.109919586 + 0.0681818182 = -1.0417377678 x = -1.0417377678 Simplifying x = -1.0417377678Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1781014042, -1.0417377678}
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