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Simplifying 14b2 + 4b + -3 = 0 Reorder the terms: -3 + 4b + 14b2 = 0 Solving -3 + 4b + 14b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.2142857143 + 0.2857142857b + b2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2857142857b + 0.2142857143 + b2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + 0.2857142857b + b2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + 0.2857142857b + b2 = 0 + 0.2142857143 0.2857142857b + b2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 0.2857142857b + b2 = 0.2142857143 The b term is 0.2857142857b. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857b + 0.02040816328 + b2 = 0.2142857143 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857b + b2 = 0.2142857143 + 0.02040816328 Combine like terms: 0.2142857143 + 0.02040816328 = 0.23469387758 0.02040816328 + 0.2857142857b + b2 = 0.23469387758 Factor a perfect square on the left side: (b + 0.1428571429)(b + 0.1428571429) = 0.23469387758 Calculate the square root of the right side: 0.484452142 Break this problem into two subproblems by setting (b + 0.1428571429) equal to 0.484452142 and -0.484452142.Subproblem 1
b + 0.1428571429 = 0.484452142 Simplifying b + 0.1428571429 = 0.484452142 Reorder the terms: 0.1428571429 + b = 0.484452142 Solving 0.1428571429 + b = 0.484452142 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + b = 0.484452142 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + b = 0.484452142 + -0.1428571429 b = 0.484452142 + -0.1428571429 Combine like terms: 0.484452142 + -0.1428571429 = 0.3415949991 b = 0.3415949991 Simplifying b = 0.3415949991Subproblem 2
b + 0.1428571429 = -0.484452142 Simplifying b + 0.1428571429 = -0.484452142 Reorder the terms: 0.1428571429 + b = -0.484452142 Solving 0.1428571429 + b = -0.484452142 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + b = -0.484452142 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + b = -0.484452142 + -0.1428571429 b = -0.484452142 + -0.1428571429 Combine like terms: -0.484452142 + -0.1428571429 = -0.6273092849 b = -0.6273092849 Simplifying b = -0.6273092849Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.3415949991, -0.6273092849}
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