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Simplifying (5b2 + -2b + -6) + -1(-9b2 + 3b + 2) = 0 Reorder the terms: (-6 + -2b + 5b2) + -1(-9b2 + 3b + 2) = 0 Remove parenthesis around (-6 + -2b + 5b2) -6 + -2b + 5b2 + -1(-9b2 + 3b + 2) = 0 Reorder the terms: -6 + -2b + 5b2 + -1(2 + 3b + -9b2) = 0 -6 + -2b + 5b2 + (2 * -1 + 3b * -1 + -9b2 * -1) = 0 -6 + -2b + 5b2 + (-2 + -3b + 9b2) = 0 Reorder the terms: -6 + -2 + -2b + -3b + 5b2 + 9b2 = 0 Combine like terms: -6 + -2 = -8 -8 + -2b + -3b + 5b2 + 9b2 = 0 Combine like terms: -2b + -3b = -5b -8 + -5b + 5b2 + 9b2 = 0 Combine like terms: 5b2 + 9b2 = 14b2 -8 + -5b + 14b2 = 0 Solving -8 + -5b + 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'. -0.5714285714 + -0.3571428571b + b2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -0.3571428571b + 0.5714285714 + b2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -0.3571428571b + b2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -0.3571428571b + b2 = 0 + 0.5714285714 -0.3571428571b + b2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -0.3571428571b + b2 = 0.5714285714 The b term is -0.3571428571b. Take half its coefficient (-0.1785714286). Square it (0.03188775511) and add it to both sides. Add '0.03188775511' to each side of the equation. -0.3571428571b + 0.03188775511 + b2 = 0.5714285714 + 0.03188775511 Reorder the terms: 0.03188775511 + -0.3571428571b + b2 = 0.5714285714 + 0.03188775511 Combine like terms: 0.5714285714 + 0.03188775511 = 0.60331632651 0.03188775511 + -0.3571428571b + b2 = 0.60331632651 Factor a perfect square on the left side: (b + -0.1785714286)(b + -0.1785714286) = 0.60331632651 Calculate the square root of the right side: 0.776734399 Break this problem into two subproblems by setting (b + -0.1785714286) equal to 0.776734399 and -0.776734399.Subproblem 1
b + -0.1785714286 = 0.776734399 Simplifying b + -0.1785714286 = 0.776734399 Reorder the terms: -0.1785714286 + b = 0.776734399 Solving -0.1785714286 + b = 0.776734399 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.1785714286 + b = 0.776734399 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + b = 0.776734399 + 0.1785714286 b = 0.776734399 + 0.1785714286 Combine like terms: 0.776734399 + 0.1785714286 = 0.9553058276 b = 0.9553058276 Simplifying b = 0.9553058276Subproblem 2
b + -0.1785714286 = -0.776734399 Simplifying b + -0.1785714286 = -0.776734399 Reorder the terms: -0.1785714286 + b = -0.776734399 Solving -0.1785714286 + b = -0.776734399 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.1785714286 + b = -0.776734399 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + b = -0.776734399 + 0.1785714286 b = -0.776734399 + 0.1785714286 Combine like terms: -0.776734399 + 0.1785714286 = -0.5981629704 b = -0.5981629704 Simplifying b = -0.5981629704Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.9553058276, -0.5981629704}
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