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Simplifying 26x2 + -59x + 16 = 0 Reorder the terms: 16 + -59x + 26x2 = 0 Solving 16 + -59x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. 0.6153846154 + -2.269230769x + x2 = 0 Move the constant term to the right: Add '-0.6153846154' to each side of the equation. 0.6153846154 + -2.269230769x + -0.6153846154 + x2 = 0 + -0.6153846154 Reorder the terms: 0.6153846154 + -0.6153846154 + -2.269230769x + x2 = 0 + -0.6153846154 Combine like terms: 0.6153846154 + -0.6153846154 = 0.0000000000 0.0000000000 + -2.269230769x + x2 = 0 + -0.6153846154 -2.269230769x + x2 = 0 + -0.6153846154 Combine like terms: 0 + -0.6153846154 = -0.6153846154 -2.269230769x + x2 = -0.6153846154 The x term is -2.269230769x. Take half its coefficient (-1.134615385). Square it (1.287352072) and add it to both sides. Add '1.287352072' to each side of the equation. -2.269230769x + 1.287352072 + x2 = -0.6153846154 + 1.287352072 Reorder the terms: 1.287352072 + -2.269230769x + x2 = -0.6153846154 + 1.287352072 Combine like terms: -0.6153846154 + 1.287352072 = 0.6719674566 1.287352072 + -2.269230769x + x2 = 0.6719674566 Factor a perfect square on the left side: (x + -1.134615385)(x + -1.134615385) = 0.6719674566 Calculate the square root of the right side: 0.819736212 Break this problem into two subproblems by setting (x + -1.134615385) equal to 0.819736212 and -0.819736212.Subproblem 1
x + -1.134615385 = 0.819736212 Simplifying x + -1.134615385 = 0.819736212 Reorder the terms: -1.134615385 + x = 0.819736212 Solving -1.134615385 + x = 0.819736212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.134615385' to each side of the equation. -1.134615385 + 1.134615385 + x = 0.819736212 + 1.134615385 Combine like terms: -1.134615385 + 1.134615385 = 0.000000000 0.000000000 + x = 0.819736212 + 1.134615385 x = 0.819736212 + 1.134615385 Combine like terms: 0.819736212 + 1.134615385 = 1.954351597 x = 1.954351597 Simplifying x = 1.954351597Subproblem 2
x + -1.134615385 = -0.819736212 Simplifying x + -1.134615385 = -0.819736212 Reorder the terms: -1.134615385 + x = -0.819736212 Solving -1.134615385 + x = -0.819736212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.134615385' to each side of the equation. -1.134615385 + 1.134615385 + x = -0.819736212 + 1.134615385 Combine like terms: -1.134615385 + 1.134615385 = 0.000000000 0.000000000 + x = -0.819736212 + 1.134615385 x = -0.819736212 + 1.134615385 Combine like terms: -0.819736212 + 1.134615385 = 0.314879173 x = 0.314879173 Simplifying x = 0.314879173Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.954351597, 0.314879173}
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