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Simplifying 0 = 10b2 + 27b + -18 Reorder the terms: 0 = -18 + 27b + 10b2 Solving 0 = -18 + 27b + 10b2 Solving for variable 'b'. Combine like terms: 0 + 18 = 18 18 + -27b + -10b2 = -18 + 27b + 10b2 + 18 + -27b + -10b2 Reorder the terms: 18 + -27b + -10b2 = -18 + 18 + 27b + -27b + 10b2 + -10b2 Combine like terms: -18 + 18 = 0 18 + -27b + -10b2 = 0 + 27b + -27b + 10b2 + -10b2 18 + -27b + -10b2 = 27b + -27b + 10b2 + -10b2 Combine like terms: 27b + -27b = 0 18 + -27b + -10b2 = 0 + 10b2 + -10b2 18 + -27b + -10b2 = 10b2 + -10b2 Combine like terms: 10b2 + -10b2 = 0 18 + -27b + -10b2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -1.8 + 2.7b + b2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 2.7b + 1.8 + b2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 2.7b + b2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 2.7b + b2 = 0 + 1.8 2.7b + b2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 2.7b + b2 = 1.8 The b term is 2.7b. Take half its coefficient (1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. 2.7b + 1.8225 + b2 = 1.8 + 1.8225 Reorder the terms: 1.8225 + 2.7b + b2 = 1.8 + 1.8225 Combine like terms: 1.8 + 1.8225 = 3.6225 1.8225 + 2.7b + b2 = 3.6225 Factor a perfect square on the left side: (b + 1.35)(b + 1.35) = 3.6225 Calculate the square root of the right side: 1.903286631 Break this problem into two subproblems by setting (b + 1.35) equal to 1.903286631 and -1.903286631.Subproblem 1
b + 1.35 = 1.903286631 Simplifying b + 1.35 = 1.903286631 Reorder the terms: 1.35 + b = 1.903286631 Solving 1.35 + b = 1.903286631 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + b = 1.903286631 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + b = 1.903286631 + -1.35 b = 1.903286631 + -1.35 Combine like terms: 1.903286631 + -1.35 = 0.553286631 b = 0.553286631 Simplifying b = 0.553286631Subproblem 2
b + 1.35 = -1.903286631 Simplifying b + 1.35 = -1.903286631 Reorder the terms: 1.35 + b = -1.903286631 Solving 1.35 + b = -1.903286631 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + b = -1.903286631 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + b = -1.903286631 + -1.35 b = -1.903286631 + -1.35 Combine like terms: -1.903286631 + -1.35 = -3.253286631 b = -3.253286631 Simplifying b = -3.253286631Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.553286631, -3.253286631}
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