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Simplifying 169x2 + 26x + -1 = 0 Reorder the terms: -1 + 26x + 169x2 = 0 Solving -1 + 26x + 169x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 169 the coefficient of the squared term: Divide each side by '169'. -0.005917159763 + 0.1538461538x + x2 = 0 Move the constant term to the right: Add '0.005917159763' to each side of the equation. -0.005917159763 + 0.1538461538x + 0.005917159763 + x2 = 0 + 0.005917159763 Reorder the terms: -0.005917159763 + 0.005917159763 + 0.1538461538x + x2 = 0 + 0.005917159763 Combine like terms: -0.005917159763 + 0.005917159763 = 0.000000000000 0.000000000000 + 0.1538461538x + x2 = 0 + 0.005917159763 0.1538461538x + x2 = 0 + 0.005917159763 Combine like terms: 0 + 0.005917159763 = 0.005917159763 0.1538461538x + x2 = 0.005917159763 The x term is 0.1538461538x. Take half its coefficient (0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. 0.1538461538x + 0.005917159760 + x2 = 0.005917159763 + 0.005917159760 Reorder the terms: 0.005917159760 + 0.1538461538x + x2 = 0.005917159763 + 0.005917159760 Combine like terms: 0.005917159763 + 0.005917159760 = 0.011834319523 0.005917159760 + 0.1538461538x + x2 = 0.011834319523 Factor a perfect square on the left side: (x + 0.0769230769)(x + 0.0769230769) = 0.011834319523 Calculate the square root of the right side: 0.108785659 Break this problem into two subproblems by setting (x + 0.0769230769) equal to 0.108785659 and -0.108785659.Subproblem 1
x + 0.0769230769 = 0.108785659 Simplifying x + 0.0769230769 = 0.108785659 Reorder the terms: 0.0769230769 + x = 0.108785659 Solving 0.0769230769 + x = 0.108785659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = 0.108785659 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = 0.108785659 + -0.0769230769 x = 0.108785659 + -0.0769230769 Combine like terms: 0.108785659 + -0.0769230769 = 0.0318625821 x = 0.0318625821 Simplifying x = 0.0318625821Subproblem 2
x + 0.0769230769 = -0.108785659 Simplifying x + 0.0769230769 = -0.108785659 Reorder the terms: 0.0769230769 + x = -0.108785659 Solving 0.0769230769 + x = -0.108785659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = -0.108785659 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = -0.108785659 + -0.0769230769 x = -0.108785659 + -0.0769230769 Combine like terms: -0.108785659 + -0.0769230769 = -0.1857087359 x = -0.1857087359 Simplifying x = -0.1857087359Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0318625821, -0.1857087359}
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