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Simplifying 29x2 + 196x + 2 = 0 Reorder the terms: 2 + 196x + 29x2 = 0 Solving 2 + 196x + 29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. 0.06896551724 + 6.75862069x + x2 = 0 Move the constant term to the right: Add '-0.06896551724' to each side of the equation. 0.06896551724 + 6.75862069x + -0.06896551724 + x2 = 0 + -0.06896551724 Reorder the terms: 0.06896551724 + -0.06896551724 + 6.75862069x + x2 = 0 + -0.06896551724 Combine like terms: 0.06896551724 + -0.06896551724 = 0.00000000000 0.00000000000 + 6.75862069x + x2 = 0 + -0.06896551724 6.75862069x + x2 = 0 + -0.06896551724 Combine like terms: 0 + -0.06896551724 = -0.06896551724 6.75862069x + x2 = -0.06896551724 The x term is 6.75862069x. Take half its coefficient (3.379310345). Square it (11.41973841) and add it to both sides. Add '11.41973841' to each side of the equation. 6.75862069x + 11.41973841 + x2 = -0.06896551724 + 11.41973841 Reorder the terms: 11.41973841 + 6.75862069x + x2 = -0.06896551724 + 11.41973841 Combine like terms: -0.06896551724 + 11.41973841 = 11.35077289276 11.41973841 + 6.75862069x + x2 = 11.35077289276 Factor a perfect square on the left side: (x + 3.379310345)(x + 3.379310345) = 11.35077289276 Calculate the square root of the right side: 3.369090811 Break this problem into two subproblems by setting (x + 3.379310345) equal to 3.369090811 and -3.369090811.Subproblem 1
x + 3.379310345 = 3.369090811 Simplifying x + 3.379310345 = 3.369090811 Reorder the terms: 3.379310345 + x = 3.369090811 Solving 3.379310345 + x = 3.369090811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.379310345' to each side of the equation. 3.379310345 + -3.379310345 + x = 3.369090811 + -3.379310345 Combine like terms: 3.379310345 + -3.379310345 = 0.000000000 0.000000000 + x = 3.369090811 + -3.379310345 x = 3.369090811 + -3.379310345 Combine like terms: 3.369090811 + -3.379310345 = -0.010219534 x = -0.010219534 Simplifying x = -0.010219534Subproblem 2
x + 3.379310345 = -3.369090811 Simplifying x + 3.379310345 = -3.369090811 Reorder the terms: 3.379310345 + x = -3.369090811 Solving 3.379310345 + x = -3.369090811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.379310345' to each side of the equation. 3.379310345 + -3.379310345 + x = -3.369090811 + -3.379310345 Combine like terms: 3.379310345 + -3.379310345 = 0.000000000 0.000000000 + x = -3.369090811 + -3.379310345 x = -3.369090811 + -3.379310345 Combine like terms: -3.369090811 + -3.379310345 = -6.748401156 x = -6.748401156 Simplifying x = -6.748401156Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.010219534, -6.748401156}
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