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Simplifying 26x2 + 17x + -45 = 0 Reorder the terms: -45 + 17x + 26x2 = 0 Solving -45 + 17x + 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'. -1.730769231 + 0.6538461538x + x2 = 0 Move the constant term to the right: Add '1.730769231' to each side of the equation. -1.730769231 + 0.6538461538x + 1.730769231 + x2 = 0 + 1.730769231 Reorder the terms: -1.730769231 + 1.730769231 + 0.6538461538x + x2 = 0 + 1.730769231 Combine like terms: -1.730769231 + 1.730769231 = 0.000000000 0.000000000 + 0.6538461538x + x2 = 0 + 1.730769231 0.6538461538x + x2 = 0 + 1.730769231 Combine like terms: 0 + 1.730769231 = 1.730769231 0.6538461538x + x2 = 1.730769231 The x term is 0.6538461538x. Take half its coefficient (0.3269230769). Square it (0.1068786982) and add it to both sides. Add '0.1068786982' to each side of the equation. 0.6538461538x + 0.1068786982 + x2 = 1.730769231 + 0.1068786982 Reorder the terms: 0.1068786982 + 0.6538461538x + x2 = 1.730769231 + 0.1068786982 Combine like terms: 1.730769231 + 0.1068786982 = 1.8376479292 0.1068786982 + 0.6538461538x + x2 = 1.8376479292 Factor a perfect square on the left side: (x + 0.3269230769)(x + 0.3269230769) = 1.8376479292 Calculate the square root of the right side: 1.355598735 Break this problem into two subproblems by setting (x + 0.3269230769) equal to 1.355598735 and -1.355598735.Subproblem 1
x + 0.3269230769 = 1.355598735 Simplifying x + 0.3269230769 = 1.355598735 Reorder the terms: 0.3269230769 + x = 1.355598735 Solving 0.3269230769 + x = 1.355598735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3269230769' to each side of the equation. 0.3269230769 + -0.3269230769 + x = 1.355598735 + -0.3269230769 Combine like terms: 0.3269230769 + -0.3269230769 = 0.0000000000 0.0000000000 + x = 1.355598735 + -0.3269230769 x = 1.355598735 + -0.3269230769 Combine like terms: 1.355598735 + -0.3269230769 = 1.0286756581 x = 1.0286756581 Simplifying x = 1.0286756581Subproblem 2
x + 0.3269230769 = -1.355598735 Simplifying x + 0.3269230769 = -1.355598735 Reorder the terms: 0.3269230769 + x = -1.355598735 Solving 0.3269230769 + x = -1.355598735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3269230769' to each side of the equation. 0.3269230769 + -0.3269230769 + x = -1.355598735 + -0.3269230769 Combine like terms: 0.3269230769 + -0.3269230769 = 0.0000000000 0.0000000000 + x = -1.355598735 + -0.3269230769 x = -1.355598735 + -0.3269230769 Combine like terms: -1.355598735 + -0.3269230769 = -1.6825218119 x = -1.6825218119 Simplifying x = -1.6825218119Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0286756581, -1.6825218119}
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