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Simplifying b = 5b2 + -19b + 12 Reorder the terms: b = 12 + -19b + 5b2 Solving b = 12 + -19b + 5b2 Solving for variable 'b'. Reorder the terms: -12 + b + 19b + -5b2 = 12 + -19b + 5b2 + -12 + 19b + -5b2 Combine like terms: b + 19b = 20b -12 + 20b + -5b2 = 12 + -19b + 5b2 + -12 + 19b + -5b2 Reorder the terms: -12 + 20b + -5b2 = 12 + -12 + -19b + 19b + 5b2 + -5b2 Combine like terms: 12 + -12 = 0 -12 + 20b + -5b2 = 0 + -19b + 19b + 5b2 + -5b2 -12 + 20b + -5b2 = -19b + 19b + 5b2 + -5b2 Combine like terms: -19b + 19b = 0 -12 + 20b + -5b2 = 0 + 5b2 + -5b2 -12 + 20b + -5b2 = 5b2 + -5b2 Combine like terms: 5b2 + -5b2 = 0 -12 + 20b + -5b2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 2.4 + -4b + b2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -4b + -2.4 + b2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -4b + b2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -4b + b2 = 0 + -2.4 -4b + b2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -4b + b2 = -2.4 The b term is -4b. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4b + 4 + b2 = -2.4 + 4 Reorder the terms: 4 + -4b + b2 = -2.4 + 4 Combine like terms: -2.4 + 4 = 1.6 4 + -4b + b2 = 1.6 Factor a perfect square on the left side: (b + -2)(b + -2) = 1.6 Calculate the square root of the right side: 1.264911064 Break this problem into two subproblems by setting (b + -2) equal to 1.264911064 and -1.264911064.Subproblem 1
b + -2 = 1.264911064 Simplifying b + -2 = 1.264911064 Reorder the terms: -2 + b = 1.264911064 Solving -2 + b = 1.264911064 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + b = 1.264911064 + 2 Combine like terms: -2 + 2 = 0 0 + b = 1.264911064 + 2 b = 1.264911064 + 2 Combine like terms: 1.264911064 + 2 = 3.264911064 b = 3.264911064 Simplifying b = 3.264911064Subproblem 2
b + -2 = -1.264911064 Simplifying b + -2 = -1.264911064 Reorder the terms: -2 + b = -1.264911064 Solving -2 + b = -1.264911064 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + b = -1.264911064 + 2 Combine like terms: -2 + 2 = 0 0 + b = -1.264911064 + 2 b = -1.264911064 + 2 Combine like terms: -1.264911064 + 2 = 0.735088936 b = 0.735088936 Simplifying b = 0.735088936Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.264911064, 0.735088936}
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