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Simplifying 10b2 = 27b + -1 Reorder the terms: 10b2 = -1 + 27b Solving 10b2 = -1 + 27b Solving for variable 'b'. Reorder the terms: 1 + -27b + 10b2 = -1 + 27b + 1 + -27b Reorder the terms: 1 + -27b + 10b2 = -1 + 1 + 27b + -27b Combine like terms: -1 + 1 = 0 1 + -27b + 10b2 = 0 + 27b + -27b 1 + -27b + 10b2 = 27b + -27b Combine like terms: 27b + -27b = 0 1 + -27b + 10b2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.1 + -2.7b + b2 = 0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + -2.7b + -0.1 + b2 = 0 + -0.1 Reorder the terms: 0.1 + -0.1 + -2.7b + b2 = 0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + -2.7b + b2 = 0 + -0.1 -2.7b + b2 = 0 + -0.1 Combine like terms: 0 + -0.1 = -0.1 -2.7b + b2 = -0.1 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 = -0.1 + 1.8225 Reorder the terms: 1.8225 + -2.7b + b2 = -0.1 + 1.8225 Combine like terms: -0.1 + 1.8225 = 1.7225 1.8225 + -2.7b + b2 = 1.7225 Factor a perfect square on the left side: (b + -1.35)(b + -1.35) = 1.7225 Calculate the square root of the right side: 1.312440475 Break this problem into two subproblems by setting (b + -1.35) equal to 1.312440475 and -1.312440475.Subproblem 1
b + -1.35 = 1.312440475 Simplifying b + -1.35 = 1.312440475 Reorder the terms: -1.35 + b = 1.312440475 Solving -1.35 + b = 1.312440475 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 = 1.312440475 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + b = 1.312440475 + 1.35 b = 1.312440475 + 1.35 Combine like terms: 1.312440475 + 1.35 = 2.662440475 b = 2.662440475 Simplifying b = 2.662440475Subproblem 2
b + -1.35 = -1.312440475 Simplifying b + -1.35 = -1.312440475 Reorder the terms: -1.35 + b = -1.312440475 Solving -1.35 + b = -1.312440475 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 = -1.312440475 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + b = -1.312440475 + 1.35 b = -1.312440475 + 1.35 Combine like terms: -1.312440475 + 1.35 = 0.037559525 b = 0.037559525 Simplifying b = 0.037559525Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.662440475, 0.037559525}
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