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Simplifying 18b2 + 4b + -3 = 0 Reorder the terms: -3 + 4b + 18b2 = 0 Solving -3 + 4b + 18b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.1666666667 + 0.2222222222b + b2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.2222222222b + 0.1666666667 + b2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 0.2222222222b + b2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 0.2222222222b + b2 = 0 + 0.1666666667 0.2222222222b + b2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 0.2222222222b + b2 = 0.1666666667 The b term is 0.2222222222b. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222b + 0.01234567901 + b2 = 0.1666666667 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222b + b2 = 0.1666666667 + 0.01234567901 Combine like terms: 0.1666666667 + 0.01234567901 = 0.17901234571 0.01234567901 + 0.2222222222b + b2 = 0.17901234571 Factor a perfect square on the left side: (b + 0.1111111111)(b + 0.1111111111) = 0.17901234571 Calculate the square root of the right side: 0.423098506 Break this problem into two subproblems by setting (b + 0.1111111111) equal to 0.423098506 and -0.423098506.Subproblem 1
b + 0.1111111111 = 0.423098506 Simplifying b + 0.1111111111 = 0.423098506 Reorder the terms: 0.1111111111 + b = 0.423098506 Solving 0.1111111111 + b = 0.423098506 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + b = 0.423098506 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + b = 0.423098506 + -0.1111111111 b = 0.423098506 + -0.1111111111 Combine like terms: 0.423098506 + -0.1111111111 = 0.3119873949 b = 0.3119873949 Simplifying b = 0.3119873949Subproblem 2
b + 0.1111111111 = -0.423098506 Simplifying b + 0.1111111111 = -0.423098506 Reorder the terms: 0.1111111111 + b = -0.423098506 Solving 0.1111111111 + b = -0.423098506 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + b = -0.423098506 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + b = -0.423098506 + -0.1111111111 b = -0.423098506 + -0.1111111111 Combine like terms: -0.423098506 + -0.1111111111 = -0.5342096171 b = -0.5342096171 Simplifying b = -0.5342096171Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.3119873949, -0.5342096171}
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