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Simplifying 29x2 + 37x + 9 = 0 Reorder the terms: 9 + 37x + 29x2 = 0 Solving 9 + 37x + 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'. 0.3103448276 + 1.275862069x + x2 = 0 Move the constant term to the right: Add '-0.3103448276' to each side of the equation. 0.3103448276 + 1.275862069x + -0.3103448276 + x2 = 0 + -0.3103448276 Reorder the terms: 0.3103448276 + -0.3103448276 + 1.275862069x + x2 = 0 + -0.3103448276 Combine like terms: 0.3103448276 + -0.3103448276 = 0.0000000000 0.0000000000 + 1.275862069x + x2 = 0 + -0.3103448276 1.275862069x + x2 = 0 + -0.3103448276 Combine like terms: 0 + -0.3103448276 = -0.3103448276 1.275862069x + x2 = -0.3103448276 The x term is 1.275862069x. Take half its coefficient (0.6379310345). Square it (0.4069560048) and add it to both sides. Add '0.4069560048' to each side of the equation. 1.275862069x + 0.4069560048 + x2 = -0.3103448276 + 0.4069560048 Reorder the terms: 0.4069560048 + 1.275862069x + x2 = -0.3103448276 + 0.4069560048 Combine like terms: -0.3103448276 + 0.4069560048 = 0.0966111772 0.4069560048 + 1.275862069x + x2 = 0.0966111772 Factor a perfect square on the left side: (x + 0.6379310345)(x + 0.6379310345) = 0.0966111772 Calculate the square root of the right side: 0.310823386 Break this problem into two subproblems by setting (x + 0.6379310345) equal to 0.310823386 and -0.310823386.Subproblem 1
x + 0.6379310345 = 0.310823386 Simplifying x + 0.6379310345 = 0.310823386 Reorder the terms: 0.6379310345 + x = 0.310823386 Solving 0.6379310345 + x = 0.310823386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6379310345' to each side of the equation. 0.6379310345 + -0.6379310345 + x = 0.310823386 + -0.6379310345 Combine like terms: 0.6379310345 + -0.6379310345 = 0.0000000000 0.0000000000 + x = 0.310823386 + -0.6379310345 x = 0.310823386 + -0.6379310345 Combine like terms: 0.310823386 + -0.6379310345 = -0.3271076485 x = -0.3271076485 Simplifying x = -0.3271076485Subproblem 2
x + 0.6379310345 = -0.310823386 Simplifying x + 0.6379310345 = -0.310823386 Reorder the terms: 0.6379310345 + x = -0.310823386 Solving 0.6379310345 + x = -0.310823386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6379310345' to each side of the equation. 0.6379310345 + -0.6379310345 + x = -0.310823386 + -0.6379310345 Combine like terms: 0.6379310345 + -0.6379310345 = 0.0000000000 0.0000000000 + x = -0.310823386 + -0.6379310345 x = -0.310823386 + -0.6379310345 Combine like terms: -0.310823386 + -0.6379310345 = -0.9487544205 x = -0.9487544205 Simplifying x = -0.9487544205Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.3271076485, -0.9487544205}
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