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Simplifying 2.34x2 + -0.667x + -1 = 0 Reorder the terms: -1 + -0.667x + 2.34x2 = 0 Solving -1 + -0.667x + 2.34x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.34 the coefficient of the squared term: Divide each side by '2.34'. -0.4273504274 + -0.285042735x + x2 = 0 Move the constant term to the right: Add '0.4273504274' to each side of the equation. -0.4273504274 + -0.285042735x + 0.4273504274 + x2 = 0 + 0.4273504274 Reorder the terms: -0.4273504274 + 0.4273504274 + -0.285042735x + x2 = 0 + 0.4273504274 Combine like terms: -0.4273504274 + 0.4273504274 = 0.0000000000 0.0000000000 + -0.285042735x + x2 = 0 + 0.4273504274 -0.285042735x + x2 = 0 + 0.4273504274 Combine like terms: 0 + 0.4273504274 = 0.4273504274 -0.285042735x + x2 = 0.4273504274 The x term is -0.285042735x. Take half its coefficient (-0.1425213675). Square it (0.02031234019) and add it to both sides. Add '0.02031234019' to each side of the equation. -0.285042735x + 0.02031234019 + x2 = 0.4273504274 + 0.02031234019 Reorder the terms: 0.02031234019 + -0.285042735x + x2 = 0.4273504274 + 0.02031234019 Combine like terms: 0.4273504274 + 0.02031234019 = 0.44766276759 0.02031234019 + -0.285042735x + x2 = 0.44766276759 Factor a perfect square on the left side: (x + -0.1425213675)(x + -0.1425213675) = 0.44766276759 Calculate the square root of the right side: 0.669076055 Break this problem into two subproblems by setting (x + -0.1425213675) equal to 0.669076055 and -0.669076055.Subproblem 1
x + -0.1425213675 = 0.669076055 Simplifying x + -0.1425213675 = 0.669076055 Reorder the terms: -0.1425213675 + x = 0.669076055 Solving -0.1425213675 + x = 0.669076055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1425213675' to each side of the equation. -0.1425213675 + 0.1425213675 + x = 0.669076055 + 0.1425213675 Combine like terms: -0.1425213675 + 0.1425213675 = 0.0000000000 0.0000000000 + x = 0.669076055 + 0.1425213675 x = 0.669076055 + 0.1425213675 Combine like terms: 0.669076055 + 0.1425213675 = 0.8115974225 x = 0.8115974225 Simplifying x = 0.8115974225Subproblem 2
x + -0.1425213675 = -0.669076055 Simplifying x + -0.1425213675 = -0.669076055 Reorder the terms: -0.1425213675 + x = -0.669076055 Solving -0.1425213675 + x = -0.669076055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1425213675' to each side of the equation. -0.1425213675 + 0.1425213675 + x = -0.669076055 + 0.1425213675 Combine like terms: -0.1425213675 + 0.1425213675 = 0.0000000000 0.0000000000 + x = -0.669076055 + 0.1425213675 x = -0.669076055 + 0.1425213675 Combine like terms: -0.669076055 + 0.1425213675 = -0.5265546875 x = -0.5265546875 Simplifying x = -0.5265546875Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8115974225, -0.5265546875}
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