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Simplifying 0.0861 = 0.9344x2 + -1.0208x Reorder the terms: 0.0861 = -1.0208x + 0.9344x2 Solving 0.0861 = -1.0208x + 0.9344x2 Solving for variable 'x'. Reorder the terms: 0.0861 + 1.0208x + -0.9344x2 = -1.0208x + 1.0208x + 0.9344x2 + -0.9344x2 Combine like terms: -1.0208x + 1.0208x = 0.0000 0.0861 + 1.0208x + -0.9344x2 = 0.0000 + 0.9344x2 + -0.9344x2 0.0861 + 1.0208x + -0.9344x2 = 0.9344x2 + -0.9344x2 Combine like terms: 0.9344x2 + -0.9344x2 = 0.0000 0.0861 + 1.0208x + -0.9344x2 = 0.0000 Begin completing the square. Divide all terms by -0.9344 the coefficient of the squared term: Divide each side by '-0.9344'. -0.09214469178 + -1.092465753x + x2 = 0 Move the constant term to the right: Add '0.09214469178' to each side of the equation. -0.09214469178 + -1.092465753x + 0.09214469178 + x2 = 0 + 0.09214469178 Reorder the terms: -0.09214469178 + 0.09214469178 + -1.092465753x + x2 = 0 + 0.09214469178 Combine like terms: -0.09214469178 + 0.09214469178 = 0.00000000000 0.00000000000 + -1.092465753x + x2 = 0 + 0.09214469178 -1.092465753x + x2 = 0 + 0.09214469178 Combine like terms: 0 + 0.09214469178 = 0.09214469178 -1.092465753x + x2 = 0.09214469178 The x term is -1.092465753x. Take half its coefficient (-0.5462328765). Square it (0.2983703554) and add it to both sides. Add '0.2983703554' to each side of the equation. -1.092465753x + 0.2983703554 + x2 = 0.09214469178 + 0.2983703554 Reorder the terms: 0.2983703554 + -1.092465753x + x2 = 0.09214469178 + 0.2983703554 Combine like terms: 0.09214469178 + 0.2983703554 = 0.39051504718 0.2983703554 + -1.092465753x + x2 = 0.39051504718 Factor a perfect square on the left side: (x + -0.5462328765)(x + -0.5462328765) = 0.39051504718 Calculate the square root of the right side: 0.624912032 Break this problem into two subproblems by setting (x + -0.5462328765) equal to 0.624912032 and -0.624912032.Subproblem 1
x + -0.5462328765 = 0.624912032 Simplifying x + -0.5462328765 = 0.624912032 Reorder the terms: -0.5462328765 + x = 0.624912032 Solving -0.5462328765 + x = 0.624912032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5462328765' to each side of the equation. -0.5462328765 + 0.5462328765 + x = 0.624912032 + 0.5462328765 Combine like terms: -0.5462328765 + 0.5462328765 = 0.0000000000 0.0000000000 + x = 0.624912032 + 0.5462328765 x = 0.624912032 + 0.5462328765 Combine like terms: 0.624912032 + 0.5462328765 = 1.1711449085 x = 1.1711449085 Simplifying x = 1.1711449085Subproblem 2
x + -0.5462328765 = -0.624912032 Simplifying x + -0.5462328765 = -0.624912032 Reorder the terms: -0.5462328765 + x = -0.624912032 Solving -0.5462328765 + x = -0.624912032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5462328765' to each side of the equation. -0.5462328765 + 0.5462328765 + x = -0.624912032 + 0.5462328765 Combine like terms: -0.5462328765 + 0.5462328765 = 0.0000000000 0.0000000000 + x = -0.624912032 + 0.5462328765 x = -0.624912032 + 0.5462328765 Combine like terms: -0.624912032 + 0.5462328765 = -0.0786791555 x = -0.0786791555 Simplifying x = -0.0786791555Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1711449085, -0.0786791555}
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