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Simplifying 0.0825x2 + -0.934x + 1.885 = 0 Reorder the terms: 1.885 + -0.934x + 0.0825x2 = 0 Solving 1.885 + -0.934x + 0.0825x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0825 the coefficient of the squared term: Divide each side by '0.0825'. 22.84848485 + -11.32121212x + x2 = 0 Move the constant term to the right: Add '-22.84848485' to each side of the equation. 22.84848485 + -11.32121212x + -22.84848485 + x2 = 0 + -22.84848485 Reorder the terms: 22.84848485 + -22.84848485 + -11.32121212x + x2 = 0 + -22.84848485 Combine like terms: 22.84848485 + -22.84848485 = 0.00000000 0.00000000 + -11.32121212x + x2 = 0 + -22.84848485 -11.32121212x + x2 = 0 + -22.84848485 Combine like terms: 0 + -22.84848485 = -22.84848485 -11.32121212x + x2 = -22.84848485 The x term is -11.32121212x. Take half its coefficient (-5.66060606). Square it (32.04246097) and add it to both sides. Add '32.04246097' to each side of the equation. -11.32121212x + 32.04246097 + x2 = -22.84848485 + 32.04246097 Reorder the terms: 32.04246097 + -11.32121212x + x2 = -22.84848485 + 32.04246097 Combine like terms: -22.84848485 + 32.04246097 = 9.19397612 32.04246097 + -11.32121212x + x2 = 9.19397612 Factor a perfect square on the left side: (x + -5.66060606)(x + -5.66060606) = 9.19397612 Calculate the square root of the right side: 3.032157008 Break this problem into two subproblems by setting (x + -5.66060606) equal to 3.032157008 and -3.032157008.Subproblem 1
x + -5.66060606 = 3.032157008 Simplifying x + -5.66060606 = 3.032157008 Reorder the terms: -5.66060606 + x = 3.032157008 Solving -5.66060606 + x = 3.032157008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.66060606' to each side of the equation. -5.66060606 + 5.66060606 + x = 3.032157008 + 5.66060606 Combine like terms: -5.66060606 + 5.66060606 = 0.00000000 0.00000000 + x = 3.032157008 + 5.66060606 x = 3.032157008 + 5.66060606 Combine like terms: 3.032157008 + 5.66060606 = 8.692763068 x = 8.692763068 Simplifying x = 8.692763068Subproblem 2
x + -5.66060606 = -3.032157008 Simplifying x + -5.66060606 = -3.032157008 Reorder the terms: -5.66060606 + x = -3.032157008 Solving -5.66060606 + x = -3.032157008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.66060606' to each side of the equation. -5.66060606 + 5.66060606 + x = -3.032157008 + 5.66060606 Combine like terms: -5.66060606 + 5.66060606 = 0.00000000 0.00000000 + x = -3.032157008 + 5.66060606 x = -3.032157008 + 5.66060606 Combine like terms: -3.032157008 + 5.66060606 = 2.628449052 x = 2.628449052 Simplifying x = 2.628449052Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.692763068, 2.628449052}
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