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Simplifying 25b + 11 = -7b2 Reorder the terms: 11 + 25b = -7b2 Solving 11 + 25b = -7b2 Solving for variable 'b'. Combine like terms: -7b2 + 7b2 = 0 11 + 25b + 7b2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.571428571 + 3.571428571b + b2 = 0 Move the constant term to the right: Add '-1.571428571' to each side of the equation. 1.571428571 + 3.571428571b + -1.571428571 + b2 = 0 + -1.571428571 Reorder the terms: 1.571428571 + -1.571428571 + 3.571428571b + b2 = 0 + -1.571428571 Combine like terms: 1.571428571 + -1.571428571 = 0.000000000 0.000000000 + 3.571428571b + b2 = 0 + -1.571428571 3.571428571b + b2 = 0 + -1.571428571 Combine like terms: 0 + -1.571428571 = -1.571428571 3.571428571b + b2 = -1.571428571 The b term is 3.571428571b. Take half its coefficient (1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. 3.571428571b + 3.188775511 + b2 = -1.571428571 + 3.188775511 Reorder the terms: 3.188775511 + 3.571428571b + b2 = -1.571428571 + 3.188775511 Combine like terms: -1.571428571 + 3.188775511 = 1.61734694 3.188775511 + 3.571428571b + b2 = 1.61734694 Factor a perfect square on the left side: (b + 1.785714286)(b + 1.785714286) = 1.61734694 Calculate the square root of the right side: 1.271749559 Break this problem into two subproblems by setting (b + 1.785714286) equal to 1.271749559 and -1.271749559.Subproblem 1
b + 1.785714286 = 1.271749559 Simplifying b + 1.785714286 = 1.271749559 Reorder the terms: 1.785714286 + b = 1.271749559 Solving 1.785714286 + b = 1.271749559 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + b = 1.271749559 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + b = 1.271749559 + -1.785714286 b = 1.271749559 + -1.785714286 Combine like terms: 1.271749559 + -1.785714286 = -0.513964727 b = -0.513964727 Simplifying b = -0.513964727Subproblem 2
b + 1.785714286 = -1.271749559 Simplifying b + 1.785714286 = -1.271749559 Reorder the terms: 1.785714286 + b = -1.271749559 Solving 1.785714286 + b = -1.271749559 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + b = -1.271749559 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + b = -1.271749559 + -1.785714286 b = -1.271749559 + -1.785714286 Combine like terms: -1.271749559 + -1.785714286 = -3.057463845 b = -3.057463845 Simplifying b = -3.057463845Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.513964727, -3.057463845}
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